How do I change my Childs Apple ID

There isn't an age restriction is this article. Note the restrictions in the article.

Apple ID Name Change.        

 What to do after you change your Apple ID or password - Apple Support    I suggest doing this before you change your Apple ID or password.

If the child is at least 13, change it in their Apple ID account. (Apple ID Account https://appleid.apple.com/#!&page=signin)