Would you claim the dog has no belief/value distinction?

Actually, I think I would. I think that pretty much all nonhuman animals would also don't really have the belief/value distinction.

I think that having a belief/values distinction requires being at least as sophisticated as a human. There are cases where a human sets a particular goal and then does things that are unpleasant in the short term (like working hard and not wasting all day commenting on blogs) in order to obtain a long-term valuable thing.