I created a short but charming playlist for Bunny Kingdom over at Melodice: https://melodice.org/playlist/bunny-kingdom-2017/
In case others add to the list at some point, here are the ones I started with:
Beethoven: 5 Pieces for Musical Clock, WoO 33 [sounds like bunnies hopping around]
Bugs Bunny's Crazy Castle (NES) Stage Theme (1)
Bugs Bunny's Crazy Castle (NES) Stage Theme 3
Cat Quest OST - Adventure Kitten
I looked up Looney Tunes music, but most of what I found is just the classical stuff that was featured in the cartoons and songs with lyrics in them (which I try to avoid for Melodice because I find them distracting while gaming).
For anyone who may be familiar with Cat Quest -- I did ask Gentlebros if they would put one more track ("A Feline Epic") on YouTube (so I could add it to this playlist). The whole soundtrack is on Bandcamp too.