Reposting an answer I made a while ago on a similar thread:
The only ones that would fit your requirements would be
Teraurge or
Monster Addict, but the first is focused on monsters rather than animals, and the other is a barebones Pokemon fangame.
If you're really desperate about that kind of content, there's
Sexy Mythical Beast Adventure, but it's really bad with some broken mechanics and a lot of bugs, I don't recommend it at all.