If a person is at substantial risk from a dog, virtually every jurisdiction would allow deadly force against the animal.
I say "virtually" because some one will surely come up with some sort of exception, though I can't really imagine it in legal terms.
Deadly/physical force laws are directed at force against humans. The only laws that really apply to defending against a dog would be animal cruelty laws, in most cases.
Regardless, the standard for justification is going to be a lot lower than it would be against a human. In the scenario of a direct, "in-progress" attack, a person would certainly be justified in shooting the dog.
Still happily answering to the call-sign Peetza.
You do not HAVE a soul. You ARE a soul. You HAVE a body.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.