* Kid (not an animal, but a close rhyme)
* Did (not an animal, but a close rhyme)
* Bidd (not a common word, but it rhymes)
* Brid (not a common word, but it rhymes)
You could also get creative and use words like:
* Quid (a slang word for a pound, but it sounds similar)
* Crid (not a real word, but it rhymes)
Let me know if you'd like to try finding more rhymes!