I have a German Shepherd dog and two free roam bunnies. I introduced the first bunny and the dog slowly, taking care to make it very very clear to the dog that the rabbit was NOT a toy, but a family member in his own right. It helped that my dog was 3 years old and obedience-trained.
With the second bunny the whole process went faster, much because my dog by then was an experienced bunny- sibling and knew that bunnies are to be respected. This has worked out fine for several years now, but the bunnies have refuges where they can run to and where the dog can’t reach, if they should ever need to take refuge from her. I haven’t been able to stop my dog from stealing the rabbits’ food though, but she won’t touch hay and as long as they have hay, they are fine even if she steals their kale (which she does if I turn my back) =)

Many BBers have dogs and cats as well as bunnies.

I have always just had bunnies and cats. When we got our first bunny, Stormy, we were worried about the cats scaring him. We should have been worried about the cats. He instilled a fear of bunnies in my cats! He loved to chase them out of “his” living room and would go after their tails if they were laying down. One cat, in particular, he liked to pick on. Never any injuries to either, though. Now that Stormy has passed on, my current 2 buns and 2 cats pretty much just ignore each other. Sometimes Bindi (bunny) will try to get Andy (cat) to groom him but Andy just looks confused and runs away.

My Mom had a Shih-Tzu who adored bunnies. She would act very motherly to them. She was the same when I was younger with my gpigs and hammies. Mom’s Westie, however, is not allowed anywhere near my buns. She has a very high prey drive and kills birds.