This is old I know but USCIS sent my 10 year old a notice on how to set up an online account which we did. Not sure why yours says 14 and above. We filed her N600 online with no issues under her account.
Your child will automatically derive US citizenship when you are naturalized (I.e. successfully complete interview and oath ceremony) assuming the child is still a minor when you finish which seems likely since she is only 8. When you finish your naturalization and have your certificate you can apply for a U.S. passport for yourself and your daughter. You can also file the N600 at that time to get your daughter a certificate of naturalization.
