There are no breeds of dogs who are guaranteed not to be a danger to your bearded dragon. Bigger dogs of course have the more risk simply because if they do decide to bite, they are more likely to instantly kill with a bite, even a playful one.
A slow introduction and never leaving your bearded dragon and dog or cat alone with your bearded dragon is the only way to be sure no 'accidents' can happen. The dog may not even intend to cause harm but just wanting to play and bearded dragons are not play toys for dogs and can be severely hurt and killed.
Puppies I would keep away from bearded dragons and other reptiles simply because puppies are more playful, daring and chew on anything and have a higher risk of causing harm to a bearded dragon.
I know many people never had problems with furry pets getting along with their scalely pets but there are just as many who post about the cat which broke through the screen of their lizard cage (either just lying ontop or trying to get at the lizard), dogs who have bit lizards or knocked over heat lamps etc. so I definitely recommend caution. Never leave the dog along with a reptile, especially if its out of its cage (a 5' iguana may not be threatened by a rat sized dog, but a dog the same size, definitely. A bearded dragon, on the other hand, is much smaller and more inclined to freeze than run).
With larger dogs, I definitely recommend not leaving them alone in the same room as your cages, keep him in a crate or another room when you are away for the day. When you are in the same room with the dog, then you can take out your bearded dragon, maybe have a spouse or other house mate handy to control the dog should it act aggressively towards the bearded dragon.
In the long run, it will depend on the individual personality of the dog and bearded dragon on whether both get along fine.
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PHLdyPayne