This past season I had my .45 Colt with me. The buck I saw came with-in 10 yards and I know I could have killed it.
The only reason I did not kill it was that he had only three points on each side. My state requires at least four on one side. I think the deer knew that. I think he felt safe. I also think he was a smart @## and wanted to rub it in. I also think he stood there to warn other deer away from my position. I really hated that deer!
Get a feel for the handgun and the ammunition you want to hunt with. Practice shooting at a target (I like the beer can idea) about the right size of the kill zone and you'll know when you are ready to hunt with a handgun.