If you like that concept for a game, years and years ago there was a game called Dogz and Catz (separate games), there were 5 versions of the game released. You could buy Dogz and Catz separately (just Dogz, or just Catz), or buy both and have your dogz and catz interact with one another. In versions 3 - 5 you can even breed your dogz and catz with each other (catz to catz and dogz to dogz, no interspecies breeding ) to have litterz of kittenz and puppiez.

And yes, everything is spelled with a z... ;P

It was a cute game, I was addicted to it for years, it was actually the reason I got into HTML and webdesign as my first website I ever created was for this game.