I am taking my 7 year old son muzzleloader hunting this year for the first time. He handles firearms very well and shoots even better. With that said, he does not handle the gun once it is loaded. I get him ready, then I set the hammer in the firing position. He knows what to do, but accidents can happen when a child is excited. He has been on every hunting outing with me since he was 3 and has bow hunted last year and this year. He impressed me this year when he let down on a deer at 24 yards. He said it was too far away.
I would say that it really depends on the kid and the situation. We hunt on our private farm, so we know that nobody should be there. I say should because you never know if you have someone trespassing or not. I am sure that he is mature enough and properly trained to use a gun. He has put more shots through his muzzleloader than any of my adult friends.
In Ohio we have an apprentice license for new hunters. They can only get it two times and must hunt with a licensed hunter. This has worked well for our situation and next year he will take the hunters safety course to get his full license. Does this mean I will let him hunt on his own?? Heck no, it will be many many years before that happens.