My 2 1/2 year old daughter came out with me grouse and deer hunting this year. She was "Daddys dog handler" for grouse. I didn't do any shooting, but we had a blast. She saw her first deer hanging this year, she walked up to it and said, "Oh my, he's big." then thought about it for a minute and said "He'll be delicious." She LOVES goose stew and venison peperettes, and knows exactly where they came from. Next year she'll be in the goose blind at least a few days.
As to when it's allowable for kids to hunt with their own firearm, as long as you keep it off the radar (ie private land or waaaaay off the beaten path), as soon as they are mature enough. I carried a .410 with slugs for coyotes when I was 10 (I wonder if I would ever have hit one if I had gotten a shot off, we hunted them with hounds so they were making good time LOL), and a .22 for bunnies well before that.