I find that there are three options when you get brainstuck like this:
1. Discard realism entirely. Don't let yourself worry about the genetics or anything because it's magic, who cares, let your dudes have detached limbs, glitter breath, and soft drinks as heads. This is easier with things that look less like real things, I find.
2. Embrace realism, hard. Whether it's to the extent of tracking genetics is up to you (I've seen realistic species that don't do that), but a good tip for if you do do that is to look at how genetics of real species work and decide what traits are dominant, recessive, if there's incomplete or co-dominance, all sorts of things. Don't limit yourself to just animals there, either; if you want whimsy with a realistic species, consider symbiosis.
3. Robots (or golems, or animated snowglobes, whatever fits). Genetics and evolution stop mattering when it's literally created and doesn't reproduce. Related to point 1, save that you can let yourself worry about the realism of balance and stuff.