What type of medium should I use? Fondant, gum paste, 50/50, clay? I keep getting cracks in my dough when there shouldn't be any. Any tips?

I love modeling chocolate.

It depends on how big the dog is. I've done small ones using fondant and some using fondant w/GumTex added.
They were on the small to medium side.
If you're getting cracks then you need to add some egg white &/or a bit of shortening to the dough. Without knowing the recipe/medium you are using I can't advise which for sure.