Animania's alterations to most mobs are not supported by this mod, basically making pet carriers useless.

Hello. I guess it will be better to ask "Animania" developer for support instead of me.
Current version of an API of the Sophisticated wolves mod allows to use pet carriers for any other mobs.

API : https://github.com/NightKosh/Sophisticated-wolves-API/tree/master/sophisticated_wolves/api/pet_carrier

Example(cat) : https://github.com/NightKosh/Sophisticated-wolves/blob/master/src/main/java/sophisticated_wolves/item/pet_carrier/CatPetCarrier.java
Example(chicken) : https://github.com/NightKosh/Sophisticated-wolves/blob/master/src/main/java/sophisticated_wolves/item/pet_carrier/ChickenPetCarrier.java

It looks like there is a bug with non tameable animals. #69
It will be fixed in next release.
Fixed