For a dog to be healthy it would need some vitamins and minerals that rabbit doesn't provide. And it would also need some fruits and vegetables. But if you did do it, you'd probally 8 or 9 does (so 7+ kits) breeding each rabbit every 2 months.
I had a Golden Retriever, a rescue 8 year old that was in bad shape when I got her. She wasn't underfed, just weak and poorly. I fed her 1/2 of a medium-size rabbit on most days, and dog food otherwise. She recovered and spent the next 5 years in good shape. She would eat everything of a fresh rabbit, bones and all, except the intestines. I learned later that wolves don't eat the intestines either.