From the american airlines website:
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 current rabies vaccination for dogs over 12 weeks old and some require proof of rabies vaccination for cats.
here's all the info you'll need:
http://www.aa.com/aa/i18nForward.do?...horEvent=false