You are right, age has nothing to do with trading but letting them trade just because they have knowledge is not a good reason. Knowledge is about theory (mostly), while trading is not only about theory. Many other things are involved, emotional control while dealing with complicated situation, time management, money management, etc.

You may allow your kids but you have to monitor them, or dont let them to do trade alone. You need to accompany them anytime they want to trade till you are sure when they can do it themselves wisely.