Meliaka is quite right. The difference is miniscule. In formal English, however, "small" is related to size only. "The house is small". "Little" refers to quantities. "We had little food left after the crash". In the case of an animal, "little" would be more likely to relate to age. See http://www.italki.com/answers/question/156250.htm

Either one. It's a small animal. The animal is very small. The animal is little. It's a little animal. All of these are correct.

In addition to the other answers given, it may depend on the context. If you are talking about a vet who only treats "little" animals and not larger animals such as horses, you refer to them as a "small animal vet". You wouldn't say a "little animal vet".