I will dump a jumble of ideas on you, most of them unrelated to the question you asked in your OP. :-)
Your daughter wants good loyal understanding mature friends and hasn't found them at her current school. She hopes to find some at a different school. But teen friendships are tricky. Many young people live under the constant fear of ostracism if they put a foot wrong at school, for example by sticking up for someone who's being bullied. They are primed to care deeply about their social standing. What's more, if they attend school for 30 hours a week then the school peer group becomes their whole world. Even setting aside the challenges presented by the school environment, there's the fact that teens are undergoing massive changes. At times, they may be too rocked by their own earthquakes to muster energy and empathy for helping friends through tough situations.
Our society tends to exclude teens, pushing them into age-segregated schools and clubs, where we expect them to make friends with others of just the same age. We don't welcome or value them in wider society as they try to take their first steps into the adult world. In law they are classed as children. Many everyday tasks remain off-limits to them until they are 16 or even 18. Parents are often suspicious of the motives of teens who associate with younger children, fearing they may be a bad influence. I think this has a disastrous effect on young people's self-esteem and on their competence.
I wonder whether your daughter would benefit more from spending plenty of time with younger and older people, rather than pinning all her hopes on teen friendships. For example, she could play with young cousins, volunteer to work with Brownies or Guides, or babysit for your friends' children. Younger kids are almost guaranteed to look up to her and respect her unconditionally, not least because they themselves are deprived of the regular company of teens which they crave. They won't judge her, reject her, laugh at her, or turn on her in the way her peers may. Likewise, she could seek out opportunities to associate with adults. She could help an elderly neighbour with gardening, deliver library books to housebound people, serve meals to homeless people, learn ballroom dancing at an afternoon class, join the WI, work as a conservation volunteer or in a charity shop, or sing with a choir which is mostly adults.
My teen did many of the above activities. She found herself received warmly by adults (especially elderly people) who longed to share their perspective and time with a young person but who found themselves usually unwanted and excluded from that role. Often she was treated as the equal of the adults, and at times she even took on leadership roles, which proved to her that she was a capable person. Some of the adults became her friends; others didn't, but there was almost none of the two-faced nastiness which is so prevalent at school. This meant she could relax, be herself, and trust people.
She did have teenaged friends, albeit from a wider age and gender range than is usual at school. (Whoever heard of a 16yo girl being friends with a 13yo boy? But if both love Minecraft, why not?) It's good to spend time with people who are undergoing similar experiences. Teenaged friends are great fun. However, teens formed just one part of her social circle, so they lacked the power to inflict extreme fear or deep misery. She felt well rooted in society, with many people on whom she could rely.