There is no need to change the DOB, and there is no need to have the DOB showing anywhere on the profile either (which is the best way for a teen anyway).
The rules for a young teen should be
only accept or invite people who you actually know, in real life, and who are friends.. not just every random stranger in an attempt to look like you have a zillion friends..
set your profile as private, so that nobody can contact you, or search for you unless you know them, tell your friends you will send them a friend invite.
do not put up photos that you know can be seen by anyone, unless you are happy with anyone seeing them, and do not try to make yourself older by pouting at a mobile phone or in a mirror, as you look ridiculous! 
To be honest, once those rules are applied, then there should not be any problems.
As a parent monitoring this, you should know the names of their friends, and be able to access your childs account to ensure there are no dubious private messages, cyber bullying, or any other actions that look suspect.