Pretty late in replying, so I'm hoping that your first summer built lots of rich happy memories for you and your family.
We actually bought Carnaby to live aboard when my daughter was 5 years old. (In 1984.) So glad we did. The boat is still her spirit home, and she still succeeds at doing things at the tiller that I wouldn't even attempt.
As other sailors have commented, surviving to tell the tale is really of first importance, but trying to make sure that everyone isn't too seasick or cold, or bored or scared to dampen the fun really is also essential. Serious consideration of gear is a necessary and ongoing concern, but nurturing the right attitude is also key. For us, figuring out some rules and training them ahead of time with "why"s was very helpful. Rule #1 was the lifejacket, which was put on at the marina gate, and worn continuously unless she was below decks in calm and predictable conditions. This was so important that it was the only rule actually given a number, but a strong candidate for Rule #2 was "obey the captain." All through everyday living, we tried to consistently model and teach the difference between all the regular teasing that goes on and a directive from the captain. A couple of times, we explicitly practiced "obeying orders" just for practice, but it didn't take much. Jen quickly learned the contexts and the tones that said "obey now, and ask later." It didn't hurt if, "Sit there," was accompanied with "until we are out of the slip and in a clear channel," or "until the boom comes across." But the main thing was for her to recognize that there was a good reason for directives, and to have her buy in. Clear and firm, but no Jekylls, Hydes, or Captain Blighs! Another important rule was to have all kinds of fun, but never use a distress call unless you mean it. I still remember a day when I heard her scratchy little voice calling "Man overboard". I am afraid that I responded fully imagining that I would be giving her a reprimand for playing with a serious thing. However, it turned out that she was in the water. The distress message was in fact absolutely apt. (Note: She had fallen into a muddy river with a significant current. This occurred at a live-aboard marina at dinner time on a sunny day, and yet I was the only one that heard her! What a mix of feelings: embarrassment that I had doubted her, pride at the way she had handled herself and the situation, & all of that mixed with the parental shock and guilt over how bad this could have become.). Needless to say, it is really important for children to develop a practical understanding of what emergencies might occur and how to respond. She began practicing early, and actually earned her RORC-Marine radio licence at the age of 9. The next rule down the list was to report possible problems. It was not only safer to have extra eyes paying attention to things that didn't look or sound or smell right, but inviting her to participate in keeping things on an even keel helped her understand that she was a valued and useful member of the crew and not just a passenger.
Along these lines, we also set up a checklist of skills that a young person would need to acquire to become "Captain of the Dinghy." This was a motivator as well as a lot of fun (and a source of pride).
If there is a bottom line to these observations it is that, while it is fundamental to keep a weather eye on all your gear and to design out as many possibilities for catastrophe as possible, putting a little focus on developing a happy attitude and skills is also very worthwhile.
Happy sailing!
j