Ok, talked to a AA rep ... Few things you would have to do:
1: You would have to call the airlines designated cargo line to let them know your intentions of sending an animal.
2: There can NOT be any dry ice what so ever in the cargo belly of the aircraft.
3: There can NOT be another animal already being transported. He wasn't real sure if it was just another dog, or any animal.
4: The carrier would have to be airline approved. Based on the carriers I've seen, your normal polymer plastic carriers with the metal swing gate is what's mostly used.
Finally, he did say that it was pretty expensive, at least with American - sending a dog usually starts around $400. Of course it may be significantly cheaper with other airlines. Here all we have is Southwest, American Eagle, & Continental Express.