I wouldn't use any handgun for deer beyond the distance where I could consistently shoot 2" groups. For me, that would be about 15 yards.
A .45 ACP will certainly kill a deer if shot into the heart-lung area, but you may have to track him down, after dark, and unless you are very patient or very experienced, that can be quite difficult. If I had to use a .45 ACP, I would want to be very close, say 10 yards, and have a perfect broadside shot.
Personally, if I intended to handgun hunt, I would want .44 magnum, for it's accuracy and power at longer ranges.