Looks like a very uncomfortable way to walk the dog. A little 4 inch streamlight flashlight is all I need to walk the dog and if I'm walking the dog stopping power isn't an issue. Your never gonna beat the .45 Colt with good old fashioned ball ammo for stopping power at a good price. Stopping power is situational. I guess a 1 oz copper solid has more stopping power than a .223.5.56 but I am equally afraid of both.
My dog walking weapon of choice has been an N. American Arms 5 shot .22 magnum single action revolver for years. You drop it in your pocket like a pocket knife. I live in the burbs so I'm just thinking yotes but I'll tell you the .22 magnum round is an angry little bee. N.A. Arms just came out with a break action model so you don't have to pull the cylinder pin to load Sweet little gun but if I have to reload a .22 I'm screwed anyway.