I’m a little surprised a .22 stopped a pit bull in full rage.
Applying the bullet in the right place, it will work very nicely. We used to butcher our own beef and my dad would put one .22 between the eyes of a 1000# animal dropping it in its tracks.
That pistol looks like my Ruger Single Six...it’ll also handle .22 magnum; with hollow points, probably three times more clout than your basic .22 LR.