It's your call to draw & bring the handgun to low ready or not. Personally I favor doing so, in spite of all the arm-chair attorneys around my neck of the woods who tell me I'll be arrested for brandishing. I'd rather be arrested and deal with it court than deal with repairing bite wounds and getting prophylactic rabies shots, but then that's just me.
What I really become upset about is that a lot of folks do not make reports to Animal Control about the dog that broke loose from its restraints and charged them. No matter how puny-seeming the rope or chain or ribbon may look to you, the person in chage of the animal must have considered it sufficient to restrain it. Either that or they are recklessly negligent. (Take your pick, but remember that options such as stupid, ignorant, dumb, idiotic, etc. are NOT available.)
Now I'm not suggesting that everybody whose dog/cat/gerbil gets loose be locked up for violating the leash law. But I am suggesting that a formal complaint filed with Animal Control that possibly results in a visit from the Dog Catcher to warn them to keep Montesque restrained or face the consequences might prevent a future episode. And if there ever is a future epsode there will be a paper trail to support the contention that the owner was more or less negligent than cognitively challenged about the restraining ability of that 1/16th-inch sisal twine holding a 150-pound+ Rottie to the tree.
BTW - I am informed by some folks who claim to have the expertise to say so that either foam- or stream-type OC spray is effective on dogs and easier to get on target than a handgun round. I'm just passing on their commentary - All I know is based on observing one episode of a prison inmate who tried the "stuff your fist down the dog's throat" trick who ended up missing an index finger. (Kong, the dog, had the good sense to spit it out when recalled by his handler.) (No, nobody even considered trying to find out if it could be reattached.)
stay safe.