I don't think it's the size of the dog that matters. It could be a 5 pounder or a 100 pounder. A lot depends on the dog/puppy itself. It's disposition.
There is no way of knowing what your puppy will be like until it's had time to grow, learn and be trained. Even the best trained and sweetest tempered dogs should NEVER be left unattended when birds are out. Even if they don't mean to hurt the bird, it can most certainly happen. Just by placing their big ole paw on it "playing"
Your best bet is to find a safe place out of reach of your new dog. On top of the refrigerator is NOT an option. It's a terribly spot for a bird cage. Too much cooking and odors and even temp changes. Not to mention grease etc.
Like you said yourself..puppies(and this one is going to be a big one LOL) are rambunctious and clumsy. Be sure to find a good safe place for the cage BEFORE you get the pup. He could very well knock in to the cage or stand and send it tumbling.
How big is your bird's cage? Can it possibly be hung somewhere? Safely and securely? Can someone build a nice secure shelf to put it on? Large enough for the cage to be STABLE on it and high enough to be out of reach of dogs.
Anyway, congrats on getting a new puppy. Just be very VERY cautious.
My dog Abbey is a sweetheart and would never intentionally harm my birds..or even outside birds squirrels...any small animal. BUT I still never leave her unattended when my birds are out.It's just not worth the risk no matter how small.