How to steal someone's best friend?

First off, I won't hurt anyone's feelings by doing this.

So basically there's a girl at our school that got kicked out of her friendship group. She had NO ONE else to hang out with and I felt so sorry for her. She ended up trying out different groups, including one she ditched and one that she has been hanging with for a week so far.

I've decided I want to take her under my wing, so her rep can go up and so I can finally have one proper best friend. All my best friends are popular guys and it gets annoying.

It's currently the summer holidays in Australia, and she only hung out with the group for a week. What can I do to make it clear I want to be best friends with her?

Note: we're already really good friends, but we don't hang out.