My little brother's GF is a causing trouble, I think much more is in store.  I think she may even be lieing about her age.  I know there are places where you can do Background checks online, but is it possible to do this on a minor when you dont have the DOB?

Doubtful.  

In KY we have an online website run by my employer that is used by the courts and law enforcement to run background checks online at any time (not open to the public).  this site also lets you view juvi records but only if you have been given permission to do so, which means you work for a specific department (like my employers juvi department and some judges).  So if you state has something like that too your best bet is to find someone who works in a department that has to do with juvi's.