Many people I know own dogs and birds. My agility trainer has a lab, a bc and a parrot and they get on very good. Her lab, Vita, takes care of a bird, she tries to protect it from the owners (!) :wink:
Another my friend has an American Cocker. When she decided to buy a parrot, she was worried about their relationships too. But then she saw this scene : a crying spaniel was lying under the bed and the parrot attacked him again and again! But later they became good friends. :D