Hello. I do not consider the 9mm pistol cartridge as a "good" whitetail load for general deer hunting. That said, I've cleanly killed 6 or 7 Texas whitetails using 9mm handguns and expanding ammunition. I've passed on many more than I shot over 30 years. On broadside shots, I've had fine luck with the 124-gr. XTP over 6.0 grains Unique as well as Winchester's 127-gr. +P+. With the XTP, all broadside shots whether through shoulders, torso and one shoulder, or just the body cavity have made through-andl-through wounds. One deer required two shots, the last being a coup de grace as it was still alive when I got to it. Had the same thing happen with a hot-loaded .44 Special a few years ago.
Texas whitetails where I hunt are not that large. The largest I've killed with a 9mm pistol has been a doe @ 140-lbs. In one state-sanctioned game management plan I was part of, many were considerably smaller. Unless presented a close shot under ideal conditions, I pass with the handgun, any handgun...or rifle. I set my criteria for these and set them well within what I think I might be capable of. I have not noted any difference in reaction between deer shot with 9mm, .45 ACP, .44 Spec (handloaded), .44 magnum, or .45 Colt. If hit right and true, they usually jump, take a few steps and go down. The farthest I've had one run was about 30 yards; .45 Colt using a 255-gr. CSWC @ 950 ft/sec. I hit a bit high in the lungs or it might have fallen sooner. With any handgun, I only shoot when the deer is stationary. If it's not, I don't shoot. Placement is everything with them in my view with about any handgun. (I do cheat and have a rifle at hand for nice deer either too far out or moving, usually a .308 or .30-06.)
I don't believe I'd shoot much larger than a whitetail the size I've described with 9mm. For me, south Texas javelina have been tougher to "stop" than the whitetail. I wouldn't hunt mule deer with one. I think it helps if the animal is not excited and doesn't suspect that you are even in the same county it is, adrenaline and all that.
The high-powered rifle and "powerful" handgun offer us more options than lesser powered handguns with regard to quartering shots vs. broadside.
Best.