I was once in a shooting house with my son who was probably 12ish at the time, nearing the end of season and a big doe walked in. She was so close, probably 30 feet, she was alone and FAT.. it was like she was asking to become sausage.
I didn’t have a rifle with me as I intended to let my son shoot anything we saw but I didn’t have confidence he could turn and get the rifle out the window without spooking her, I did however have my CCW.
The trusty KAHR PM45, loaded with 230gr short barrel Gold Dot’s. I put the round just behind the shoulder, it stopped just under the hide on the other side, after busting through a rib no less. It left one the bloodiest blood trails I’ve ever seen, but the deer did run probably 40ish yards.
My confidence in my little 3” barreled KAHR grew exponentially, as did my fear of over penetration in the event of a self defense shooting. Anyway, yes you can absolutely kill a deer with a .45acp.
If you want advise on hunting with one, I’d tell you to use one with thin/target front sight, and only plan on shooting in good daylight. I vividly remember almost not taking the shot because the front sight covered half the shoulder, I amazed myself with the shot placement. Luck had a lot to do with it.