I'm sorry, I disagree. I think the dog must be found a new home immediately, as it is neither fair for Veg to have to live with a dog if she is against the idea, and unfair to the dog to live with anything less than an accepting, loving home.
In my county there hasn't been a case of dog rabies in decades, and other dog diseases aren't transmittable as far as I know to humans. Dog bites, like any other puncture or abrasion can get infected and should be washed and watched. Some dogs, especially fearful ones, are not a good match for homes with children, and that is reason enough to find the dog a new home asap.