Actually, it would be best that a child has their own Battle Net account. That way the parent/guardian can apply Parental Controls as needed. The Battle Net account can be placed in the parent’s/guardian’s name until said child comes of age and then the account can be placed in the child’s name.
Also, the child will then be able to keep any account-bound items versus losing them when they become of age and need to be moved to their own account.