I enjoy handgun hunting, with handgun loads and at handgun distances. I have both a 6" and 8-3/8" .357's I hunt with.
With hunting loads suitable for killing deer. Your going to get blast. But for me I'd rather hunt with a pistol within it's limits and sometimes not get a deer. I'd modify TCLouis's post a little, With you being in Georgia like me, the deer are a little smaller.
I'd go with a 125gr hollow-point and electronic earmuffs. When I was hunting with a pistol in PA (forever ago) I used a 158gr hard-cast SWC.
I'm just getting back into revolver deer hunting and have been practicing a lot with the 8-3/8" wow is it a tack driver.