+1 on you can't hit a charging dog in any particular spot with a handgun. I shoot target pistol, and when I was shooting in the mid 270's wouldn't have been able to reliably make that shot much past 50 feet if it was standing still. Charging I'd be lucky to hit the dog at all.

From what I understand, a handgun bullet can ricochet off a human's head at shallow angles. I would expect the same could happen with a dog's. That, and the relatively small size of a dog's head, makes a head shot a lousy choice for self defense IMO. If I were armed and attacked by a large dog, I'd have one arm trying to keep it off my throat while I was putting bullets into its chest. A contact shot through the lungs with a full load .38 is going to do a lot of damage. I'd expect the exiting round to be potentially lethal, too...would seem to be a rare good use for Glasers.

From a distance? You'd want a rifle. A handgun is a defensive weapon.

Sounds to me like your vet's given you good advice on how to put down a sick or injured dog, but not good for self defense. If you're talking about something else, consider that some people place more value on their dogs than some people do their family members, and react accordingly, for what it's worth.