I agree with the last poster. Social anxiety could be an issue.

Of course, she might also be more introverted, too--getting her energy from spending time away from people. However, even introverted people might have some close friends.

She might do better at her age with a get together with a group of girls. Perhaps you might ask her to invite several girls to some activity, such as to a good movie for kids her age. Not just one on one.

I wonder if she might be willing to talk to the school counselor. But, keep in mind that if people don't want to change and are happy with the way things are, it's hard to motivate them to seek help. Maybe the school counselor could call her in and talk about school stuff and feel her out about her social life (or lack of). A thought, anyway......

I was very shy in high school and really close to my sis, so I wasn't really interested in other friends. But when we parted, I was able to start making friends and to get close to them. It's possible her brother is currently meeting her social needs.