My upcoming move

Yes, there is a summer cut off on animal transport, and also a limit and I believe it's two animals MAXIMUM or one per-traveler. Also most flights only allow like 4 animal on any given flight and it's a first come first serve basis, so the sooner you schedule the better your chances will be. There are also certain type of dogs like snubbed nose dogs that are no longer allowed on flights. You will also need recommened carriers for your pets. But you may end up having to make a decision on which animal(s) you are going to take.

For American, it's one in-cabin pet per traveler and two in the hold. Total of three maximum possible per traveler. For three of you traveling you could conceivably carry 9 pets. Like I said a few posts ago, the two of us took five in one trip.

They allow a total of 7 pets in cabin - 2 in First Class and 5 in the main cabin. If Anushka's three year old can have an in-cabin pet, they could carry on all three of her animals.

The maximum in the hold depends upon the plane and the number and size of carriers, but I've seen them put quite a few in there.

http://www.aa.com/i18n/travelInformation/specialAssistance/travelingWithPets.jsp