It looks like Hakan K (has a super cool website where he solves all kinds of optimization problems for fun) was able to solve it using the Picat language in a very small amount of code with a solution (not sure if optimal):

http://hakank.org/picat/dogbunny_puzzle.pi

His website is a treasure trove for these kinds of problems and worth studying.

The solution is 26 steps and that should be the optimal solution.

Awesome! Thanks for popping up and clarifying.

For those of us that are not experts, how is this sort of problem generally classified? I've seen others on here say classical planning, but I wasn't sure if that is correct.

I would (also) say that this is a classic planning problem. It's deterministic, observable, static, and discrete.

I appreciate the clarification here. It helps. Thanks!