If she has friends via her activities, she'll be fine. There are also good prospects of her making friends at home education groups if the two of you are willing and able to get out to them. This is likely to involve travel, and in most areas is much easier if you have a car. Possibly 1% to 2% of kids in England and Wales are home educated (there are no reliable figures) so if you do the arithmetic you'll see there are likely to be others nearby, but of course they are somewhat thin on the ground. On the plus side, because home ed is such an efficient way to learn, they tend to have time on their hands and to be seeking friends also.
The social scene becomes somewhat more challenging in the "GCSE years". Home ed teens will still have more time available than their schooled peers, but less than when they were younger. The upshot is that they become rather more selective about how they spend their limited free time, and may take the view that it's easier to stick with existing friendships rather than seeking out new ones. From what I've observed, it's easier to join the home ed social scene at 12 than 15. So that's a reason to jump ship now rather than later.
Here's another. Trying home education now does not have to be a big commitment. You can have a go for a year or two and see whether it suits. If not, your daughter can return to school. The GCSE curriculum is largely self contained, so there isn't too much prior knowledge assumed going into Y10. But it's a different story for those joining school later. The system is so rigid that families often go to great lengths to avoid even changing school, let alone moving from home ed to school, later than the start of Y10. It is quite feasible to pull a child out at this point, but it's more a case of no going back.
And finally 😁 there's a lot for you to learn about arranging exams for HE kids. It's quite doable, but it's complicated, not least because there are more choices than at school. Which exact subjects will she do, at which exam centre? Which exam board has a syllabus most suited to her? How many will she sit and at what age? (Home ed kids tend to spread them out over several years.) Which subjects will she do first? How will she prepare for them, and which resources will she use? Will she study intensively over a year or less, or take longer? And so on. It would be nice for the two of you to settle in and get used to home ed now, when exams aren't looming. You can adopt a leisurely approach and find your feet while gathering ideas about how you want to tackle exams.
So yeah: I think now is better than later, for all these reasons. And most important, you say she's unhappy, so why put her through more? The school issues you describe don't sound fixable. Possibly a different school would work, but home ed seems the more obvious route to try first.