Your poor DD, it is a real ordeal. I went through the same kind of thing, started with low-level friendship-group bullying in year 8, sometimes they were nice then they would be utterly horrible. Then I was excluded completely from start of year 10. Socially I became a leper once my old friends had cut me out - all the girls were in groups and didnt want me anywhere near them. No one dared speak to me or come near me in case my uncoolness was contagious and they would be excluded too they certainly didnt want to be seen as welcoming a reject, as that would have tainted their own social standing. I was blanked by dozens and dozens and dozens of people, overnight. After years of bullying, my former friends literally never looked at me or spoke to me again. It was a terrible, damaging experience knowing I was forced to go to that school for another four years and the loneliness and humiliation and awfulness of it all truly ruined me. I eventually managed to form a basic friendship with some girls I knew a little bit from school clubs, but they were also fairly damaged from bullying and it wasnt a good experience. I don't think I got my mental health strength back until my mid 30s.
If someone had said to me back then, "look if this isnt working out, we can help, we can make huge changes for you, it isnt impossible and it is worth a risk to have a chance at not being sad every single day of your life", I would have wept for a week with the relief and begged for help. But no one helped me. My mum just said, "well we all fall out with friends, just keep your chin up and things will be better in a little whole." I just had to struggle on, day after day, and there were many dark days when I truly didnt want to live. It sounds melodramatic but there it is. I would never, ever put my own DD through that.
So, offer your DD some options. Ask her to give it a try until half term if you must, tell her to join lunchtime clubs and ask the librarian if she can sit in a corner and read when she is all alone (I tried that, mine said no!) Or find a quiet space to tuck herself away from the meanness and the loneliness, and in that space of time promise her you will do everything you can to find her a place at another school, any school. And also sit down with her and research options for online schooling at home. You need to give the DD some hope, not just hold her hand to the fire and force her to tough it out. Please. I doubt this is running away at the first sign of trouble, I expect there has been unpleasantness for ages and this is just the culmination of it.
I will be thinking of your DD and you, i hope you both find the strength and wisdom to decide on a path that leads to a happier life for your DD.