Be sure to look up the hunting regs in the state you will hunt in, as there are some really stupid relatively recent restrictions that might dictate your deer handgun.
Missouri, for instance, now requires the gun have at least a 6" barrel, and expanding bullets. In my early years in the state, my .44 with Keith 429421s was just fine. Not now.
I can't seem to find that, do you have a link?
