Back in 2003, the state of Georgia removed the minimum requirement for deer-legal centerfire handguns. In theory, a pocket pistol in .25ACP is legal to shoot deer with. In practice, it's about the dumbest choice of tool for the job. Given the range of legal options, though, I know of nothing unlawful or unethical about a .38spl behind the ear if necessary to finish a down deer. That said, I've yet to see a .243 through the vitals fail to do the job.
Another thing about the Georgia hunting regs... last I understood, they're worded so a hunter who has a CCW can possess their carry pistol while hunting with archery, BP, or modern firearms. They said the idea was the hunter, while hunting deer, could still defend against two-legged critters... again, picking the right tool for the job.