I introduced my girls to guns early. My intent was to take the mystery out of guns. I told them they can see / handle the guns anytime they want. We go to the safe and they can handle anything they want. BUT I talk to them and demonstrate safe gun handling skills. We talk about what to do if they find a gun or if they are at a house in which a friend shows them a gun.
When they were ready to shoot I took out my old Hunters safety stuff and reviewed it with them. Once they are old enough I will take the hunter safety class with them. In fact I am looking to become an instructors so I can teach their friends and other kids.
I bought my a CZ 452 Scout for my 9 year old last Christmas (with Mom's approval of course :-) ) She earns rounds by doing her chores, getting good grades, etc. Then we go to the range and have fun.
Another tip I got from a friend was to use .22 bird shot the first couple of times out and use moving targets or pop cans. Kids love instant feedback. It worked great.
I also put a cheap red dot on it to make it as easy as for them to hit something. When she is older I will take the dot off and start working on iron sights.
We compete against each other. She shoots of a rest and I shoot off hand. We use a dueling post. It is great practice for me and she gets a chance to beat me. I take a lot of ribbing from her when she does beat me.
This is a fun time to introduce your kids to shooting. Gets lot of advice and pick what seems right to you.
Good Luck,
North Nick