You are the one getting the dog. Most everything I read hear rings true, pay particular attention to safety.
GSP's are fast and can easily give good close chase to rabbits, careful of your shot. If you whoa break your dog
and teach him/her to be steady to shot on birds, it may work on the bunnies as well. I have hunted over GSP for about
6 years. I had one instance last year when a young female made a quick lunge hunting up a waterway and came up with
a bunny. I have had numerous opportunities to shoot bunnies while pheasant and quail hunting that would have been
safe shots while hunting over young dogs. The young dogs were semi pointing the rabbits. I don't shoot them because these dogs get finished and sold as bird dogs. The breed is however, as mentioned, completely capable of hunting fur or feathers.
My advise, start with birds and teach whoa. When you get it right do the same with rabbits. You should end up with a dog
that can handle both games. A dog that points rabbits and birds is what I would try to have. If you let the dog chase rabbits
you open up the situation to possible tragedy and it is hard to hunt with a dead dog.
Good luck with your "meat dog"!