***UPDATE ABOUT USERNAME*****
Again, this is a purely if your child wants to type thing. I'm not requiring anyone to make an account. However, if your child is really into the composing aspect of the Quaver Music website, I would suggest maybe having him/her sign up for a private account. You as the parent will receive an email that requires you to approve their sign-up. It's very, very well monitored.
You can read more under the FAQ section found on the Quaver homepage.