Step one: What do the rules say?
For example, in Oz the rules require an animal to be in a cage strong enough to prevent escape with a waterproof base, and placed in the cargo section. There's an exception for guide dogs who may travel with their user but must sit on an absorbent mat.
Years ago there was also a requirement that swine must be prevented from rooting but that was removed. The powers that be must have been successfully lobbied by the local Porcine mile high club something...