Your answer could depend on tons of factors. Can you be more specific about what's okay, and what's not? What kind of "dog" person are you (and the other members of the family)? Big/little, barking, high energy or lazy, will it be in the house alot? Many breeds of dogs bred for working around livestock don't necessarily make good "pets". They have a job. What climate do you live in? Great Pyranees is not going to thrive in hot weather, and it takes a special kind of owner to appreciate having a dog that size and furriness in the house (plus it defeats the purpose) - though they are great dogs. Also, if your new dog ends up being a nuisance rather than a help with the birds, are you willing to rehome it or contain it? You might also look into an adult dog (or a "teen") to have a better idea of what you're getting.
If there are other kids coming around, it sounds like you would appreciate a good kid dog over protectiveness, right? So maybe big enough to deter a predator without being aggressive (like a golden retriever...not sure how those are with actual pet birds - they are bird dogs), or a loud dog. Perhaps "foster" a dog and see if it's a good fit? Even so, it's a crap shoot. No guarantees. The best dog we ever had, hands down, for a job like this was a chow/aussie mix...but it's not something I would have known before owning her (and we just happened to get all of the good traits). Good luck, and take your time. Plus, ask all of the family members.
My recommendation no matter what, would be to keep the birds in a covered, predator-proof run when no one is home. Free-ranging when no one is supervising will always have risks.
