We have 10 birds and 7 dogs and for the most part everyone gets along. My smaller birds do not have their wings clipped so that they can fly away from the dogs if need be. I worry more about the bigger birds (african greys and macaw) because they can't fly away, and sometimes they get frightened and end up on the floor, but only one of my dogs every really bothers the birds. She just barks at them, has never been brave enought to actually get too close,lol. All of our birds get to come out every evening for a couple of hours, other than that they are kept in nice roomy cages with lots of toys.
Our Indian Ringneck parrot, Blue, actually has all the dogs afraid of her, cause she has bit all of them at least once for getting to close to her space in between our stove and fridge, she bites us also, you don't want to be barefoot when she is on the floor
She can also fly, but is not the least bit afraid to be down on the floor with the dogs and she is not much bigger than a cockatiel!
Anyway, I'm just trying to say, yes, you can have your birds and your dog.
Good luck and keep us posted on how things go!