I think that, by taking all this stuff she just deeply wanted to be noticed. She didn't feel like she was part of the gang because she was younger. She was overprotected by Buffy but didn't take the time to understand why, because she didn't like the situation. She wanted to be a grown-up, just like the others. And I'm pretty sure all the kids at her school thought she was weird, since she was the Slayer's sister (I guess school wasn't always easy for her). She was probably just feeling really alone.
We didn't see much of Dawn without the Scoobygang before S7, so nobody knows if she had friends or if she just knew some kids and tried to be part of a gang..