What do you mean by "backup for deer"?
I have used a .357 a couple of times to finish off a crippled deer when I didn't want to shoot it with the rifle again. It worked fine with Remington Golden Saber 125gr. midrange loads and with 180gr. hard cast bullets at just over 1000fps. If the animal is hurt bad enough that it can't get up it should be easy to get close enough for a spine shot or a head shot if the antlers aren't an issue.
If you mean a backup in case your rifle is out of commission for some reason then yes, I think it would work for that, too. However, I would prefer a longer barrel for the increase in sight radius. If this was my purpose for having it I would also prefer a bigger hole in the end.
Answering questions about if some gun/caliber combination will work at some certain range is tricky, because it assumes you can hit the vitals at that range. If you put a 158gr XTP bullet into the rib cage of a deer at 150 yards you will make venison.
If you intend to hunt with it you need to figure out how far you can consistently hit the vitals of a deer from the kind of position you will likely be using in the field. Use a 6" circle, maybe an 8" at the biggest. If you hunt from a blind with a chair and a rail to rest on then bring a similar chair and a sawhorse to the range and practice with it. If you like to stalk or still hunt then try shooting offhand, rested against the side and top of a post, from braced kneeling, and sitting. How far away can you hit that circle EVERY time? That is how far you should shoot at a deer with that handgun.
If you want a real test, find out how far can you consistently hit that circle after having sprinted 100 yards? Seems likely that when you see that 18 pt. deer it will be right after you climbed a steep hill and are out of breath.
ETA no offense to lon371 with my picking a 6" circle instead of 8". The reason is that a 6" gives you a little more margin of error, which most of need every bit we can get in the field.