one thing about GSDs (German Shepherds) they are PEOPLE dogs. They don't do well without a TON of interaction with their people, every single day. I'm not talking a few minutes, but several hours.
My youngest isn't trustworthy around the birds unsupervised. He is learning "leave it" but he still thinks the chickens are fun squeeky toys. The bunnies, well, he can't be trusted around them at all.
My oldest? He carries baby chicks back to me if they get out of their pen. He herds the bunnies if they escape. He's fine with the guinea pig and the parakeets too. Wild birds, he hates them. Wild bunnies are snacks as are squirrels, chipmunks, and mice. He hates other dogs being in his yard, but most of the livestock is outside of his fenced in yard. He does alert us to any trespassers though.
I posted this in another thread, but I'll put it here too since you are considering one of these guys
also, if you are considering a rescue GSD, make sure that it has been fostered by a knowledgeable person. GSDs are prone to several genetic diseases and temperament issues if not well-bred. A good dog with proper nerves, however, is almost impossible to "mess up" and can recover from pretty much any experience.