Found information on aa.com (American Airlines) about traveling with pets.

General Information
Pets traveling with passengers must check in at the ticket counter. No curbside or self-service check-in is allowed. Please allow extra time beyond normal check-in guidelines, but not more than 4 hours prior to your flight time.

Acceptance of Pets
Checked or carry-on pets are allowed on domestic flights in the 48 contiguous states, Alaska, Puerto Rico and USVI.

Types of Pets Allowed
Cats
Dogs (see Breed Restrictions below)
Household Birds (defined as a bird that can be domesticated and typically resides in the home. No poultry such as ducks or chickens, wild, undomesticated or birds of prey are accepted.)

Breed Restrictions
The following breeds or crossbreeds of dogs are no longer accepted as checked baggage:
American Pit Bull Terrier
American Staffordshire Terrier
Bull Terrier
Doberman Pinscher
Rottweiler
Exceptions:
Service Animals with or without a disabled passenger
Official search and rescue dogs with documentation
Official bomb/drug detection dogs with documentation
Puppies of these breeds between 8 and 12 weeks

Pets Traveling In The Cabin
See below for applicable Fees.
Charges are payable at the airport and the passenger must show the pet travel fee receipt at the departure gate.
The maximum size for cabin pet carriers is 23" long x 13" wide x 9" high. Per the Transportation Security Administration (TSA) mandate regarding carry-on baggage allowance, a pet kennel counts as a passenger's one carry-on bag.
Only one pet kennel per ticketed passenger may be accepted for travel in the cabin, as pets must go under the seat in front of you.
The kennel may contain two (2) dogs or cats but they must be the same species, ages between 8-weeks and 6-months, and weigh less than 20 lbs.
Animals must also be able to stand up, turn around and lay down in a natural position in the kennel.
Soft-sided pet carriers are accepted as long as they are constructed of water-repellent, padded nylon with mesh ventilation on two or more sides.
All animals must be a minimum eight (8) weeks old for dogs and cats.
No carry-on pets to/from Hawaii or Transatlantic/Transpacific or Central and South America.
The maximum number of carry-on kennels on American Airlines flights within the United States and Canada is seven total: two (2) in first class and five (5) in coach and/or business class. However, seeing eye/hearing service assist animals and search dogs are not counted in the maximum number allowed in the cabin.
On American Eagle and AmericanConnection®, one pet in the cabin is allowed.
Pet may not be removed from their kennel/container at any time while on-board the aircraft.
American assumes no liability for the health or well-being of carry-on pets.
Please call Reservations at 800-433-7300 to check for availability and then make a reservation for the pet.

Pets Traveling As Checked Baggage
See below for applicable Fees.
Aircraft cargo compartments are pressurized and are normally maintained at a temperature range of 50-70 degrees Fahrenheit.
Must be a minimum eight (8) weeks old for dogs and cats.
Not accepted from May 15th through September 15th due to risk of high temperatures. Also see Temperature Restrictions below.
Animals must be in separate kennels unless they are of the same species and comparable size, weigh less than 20lbs each and are between eight (8) weeks and six (6) months old.
The maximum size for checked kennels is 40" long x 27" wide x 30" high. However, the maximum size kennel is not accepted on Boeing MD-80 or Fokker 100 aircraft. The maximum weight of a checked pet and kennel (combined) cannot exceed 100lbs.
Federal Regulations require written certification from the customer that dogs/cats have been offered food and water within 4 hours (with the specific time noted) before delivery to the carrier. This certification must be securely attached to the outside of the kennel so that it may be easily noticed and read and have the customer's signature with the date and time it was signed.
Feeding and watering instructions for a 24-hour period must also be provided. Instructions of "No food or water," are not acceptable unless directed by the attending veterinarian.
Kennels must be constructed of wood, metal, plastic, similar material, leak-proof, escape proof and door must fasten securely and need ventilation on 2-sides in addition to door.
Animals must have room to stand/turn around, sit and lie down in a natural position.
Pets not accepted at departure time remain the responsibility of their owner.

Temperature Restrictions
Temperature Restrictions have been established to ensure animals are not exposed to extreme heat or cold in the animal holding areas, terminal facilities, when moving the animals between terminal and aircraft or on an aircraft awaiting departure.

Heat Restriction: Pets can not be accepted when the ground temperature is above 85 degrees Fahrenheit at any location on the itinerary (75 degrees for snub-nosed dogs and cats).
Cold Restriction: Pets can not be accepted when the ground temperature is below 45 degrees Fahrenheit at any location on the itinerary unless the pet has a veterinarian's statement of low temperature acclimation (see below). When temperatures fall below 20 degrees Fahrenheit, pets may not be checked even with a statement of low temperature acclimation.

The low temperature acclimation certificate/statement/form must include:
the name and address of the passenger
the name of the animal
name and signature of licensed veterinarian
the veterinarian's accreditation date and number
the temperature which the animal is acclimated
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Fees
The charges for transporting pets on domestic flights are based on one-way travel and are as follows:

Within the 50 United States and between the 50 United States/Canada/Puerto Rico/USVI $80.00 US / $123.00 CAD* per container
Between the United States/Canada and Mexico/Central & South America/Caribbean
$50.00 US / $59.00 CAD* per container

*Plus 7% Canadian Good and Services tax

The following applies to all destinations:
Charges are payable at the airport, American Airlines Travel Centers or Travel Agency by check, cash, credit card or voucher. If not used, the refund is to the original form of payment.
Kennel purchase price, if necessary, is in addition to above travel charges.
Charges apply for each connection segment when the voluntary stopover is 4 hours or more. Only one charge applies if a two-segment connection is less than 4 hours.
Seeing eye/hearing ear/service assistant animals and animals trained to search for victims of disaster travel free of charge. Other search dogs (example: narcotics) are accepted as checked pets only at the passenger's expense.
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Health Requirements
American does not require a health certificate for the acceptance of pets for travel in the cabin or as checked baggage within the 50 United States. However, we encourage you to contact your family veterinarian or state authorities directly for individual state requirements to avoid any possible inconvenience at your final destination.
All states require proof of rabies vaccination for dogs over 12 weeks old and some require proof of rabies vaccination for cats. American requires that the animal be vaccinated for rabies within the past 12 months.
Currently, American does not require documentation regarding the sedation of a pet, nor do we restrict sedated animals. Consult your veterinarian about the use of tranquilizers.
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Dominican Republic
Birds from The Dominican Republic are prohibited entry into the United States.

California, Virginia, Pennsylvania
Birds traveling from California or Virginia to points in Pennsylvania must be accompanied by a Pennsylvania Permit number which may be obtained by contacting:

Avian Health Division
Bureau of Animal Industry
Pennsylvania Department of Agriculture
2301 North Cameron Street
Harrisburg, PA 17110
717-783-5301
California, Nevada
Due to the confirmation of Exotic Newcastle Disease, Animal and Plant Health Inspection Service (APHIS) has imposed a federal quarantine and birds from the following areas may not be accepted as a checked or cabin pet.

California: Imperial, Los Angeles, Orange, Riverside, San Bernardino, San Diego, Santa Barbara, and Ventura Counties.
Nevada: Clark and Nye Counties
For more information see http://www.aphis.usda.gov/lpa/issues/enc/exoticnc.html .

International Travel
Carry-on pets are not allowed on Transatlantic, Transpacific or Central/South American flights. Animals traveling as checked baggage may be allowed, however, some international destinations may limit the number of animals allowed per passenger as checked baggage. Please call American Airlines Reservations at 800-433-7300 and check with the consulate of the country to which you are traveling for further details as the answer varies from country to country.

Connections to Other Carriers
Pets are not interlined between American Airlines and other carriers (including codeshare partners). Pets must be claimed and rechecked to each carrier. You will be responsible for claiming the animal and rechecking it with the other carrier.

Pets Traveling Alone
American Airlines Cargo and Priority Parcel Service ship pets to most destinations. You can find information about pets traveling without a ticketed passenger at AACargo.com, or by calling 800-CARGOAA (800-227-4622).

Hope that helps.

--Islander