I'm out of that game but I will say the American Whitetail Deer is NOT bulletproof.
A cast lead 44 projectile of 240-260 grains with a flat point or a HP, put in the right place, will easily kill a deer cleanly.
A friend of mine uses a short lever action chambered in 44 mag and he reports outstanding results with shots under 100 yards.
Another friend had an old Ruger 44 carbine and only used jacketed bullets, he also had outstanding results.
Those guns have longer barrels than a handgun but I don't think the reduction of velocity with a shorter barrel is a big deal if the ranges are reasonable.
It's just not that difficult to cleanly bring down a deer. A soft 240-260 grain flat point or HP bullet going 1000 fps or better will do the trick.
In another era, a lot of whitetail deer fell to a soft lead 36 caliber round balls travelling at much slower speeds.