We have alot of rabbits around our place, they go into the coop and clean up the food that the guinea hens bill out of the feeder onto the floor. None of our animals will bother them, but that is OK because they are cottontails and those are good eating. Just need to get my 22 sighted in.
Our German Shepherd is all about the ball - THROW IT!!! He does like to charge at the goonie hens, but just to make them fly. Once, one of them tried to run away instead of flying - and the 114 pound dog ran it over, lol. After the bird rolled a couple of times and then started squawking at him, the dog just stopped and looked at it like "You were supposed to FLY, you idiot!".
The cat doesn't seem to bother with them, but she is good at chipmunks and mice.
The English Setter is so gentle that he wouldn't dream of hurting anything, but he does like to point everything for me to see, lol. He is also too old to chase anything down at 12 years old. More into sleep at this stage of his life - and standing at the fence and barking at pedestrians, atv's, smells, swamp grass ... who knows what.