Well, it's probably a pretty good idea, if you don't mind chasing wounded deer all over the countryside.
(Or, of course, you could just wound them and then let them get away.)
The hunter owes the hunted as quick and as conclusive a death as possible.
How good are you, at head shots with a pistol?
The .45 is a close-range weapon.
How close can you get to a deer?
(Have you ever gone deer hunting?)