I moved to a different country (UK) at age 26 (but had previously done a 9-month long Erasmus). I knew one person whom I'd met at a previous job back home, but she was barely an acquaintance. We maybe met up 3-4 times in my entire first year, if that. I also have struggled to make friends my whole life and have social anxiety.
I wouldn't say it was a walk in the park, and I definitely had more barriers (new city, different language, no job, etc) than your daughter appears to have. Not going to lie, it was a rough first year, and I did spend my birthday on my own, but it was also one of the best decisions I've ever made. It changed me, it made me a more resourceful person, braver and independent.
I would encourage practically anyone to move away from home, even to another country. And especially on your own.
I know it's tough, being a parent and worrying about your child's well-being, especially when you see them suffer and struggle, but this change can only bring on good things. I would support her in her new adventure and be there for her if/when things get rough, which they very well might. You can always visit her and she you.
And worst case scenario, she returns home.