You'd be surprised how much ofa diff. dogs will make. I've got 7 beagles now and they'll burn the hide off a rabbit. Not to mention they'll jump him so I don't have to get in the briars. In terms of relocating them, I personally don't feel it will help much. I have a feeling by bringing new ones in your area, foxes/yotes will get them easier since they don't know the lay of the land and where the holes are to get away from predators. But then again, I guess it couldn't hurt to try it. I'd focus more on predator control, food, and habitat for the bunnies though. If you do this, you won't have to worry about bringing a new supply of rabbits in. Hope this helps.