My kids haven't had anxiety problems, so I don't have any first-hand experience. I have crossed paths with many teens who have. The standard advice is to give them a complete break from any enforced academic work, encourage them to do whatever makes them happy, focus on mental health, and just let them recover first. There is no particular advantage to doing exams at 16 rather than any other age. Only at school is everyone expected to do a large number of exams all at once at a set age, and labelled "behind" or a failure if they don't.
Given that you say your daughter has been barely coping, she may not be in the right frame of mind to start an online school or make any major decisions. However, once the fear of returning to school has been lifted from her, she might start to be more relaxed and ready to learn. There is no rush. GCSEs are pretty stressful for most kids, and maybe this isn't the right time for your daughter to jump into a formal programme involving deadlines which will pile more demands on her.
You could instead start off with other types of learning which don't involve assessment and producing output, but just learning. Start off with your daughter's favourite subjects to give her a boost to her confidence, and just let her explore. It doesn't have to be the sort of topics which are taught at school, and it doesn't have to lead to a qualification to be educational. Of course qualifications are often useful in the long run, but there's plenty of time for that later. I would get your daughter on an even keel first.
Through their teens, my eldest (who had a different health issue) spent a huge amount of time on self-directed art, plus various other things which interested them. They sat one GCSE at 19 and one at 20 before going to university, having been admitted via portfolio and relevant work experience. Uni is going brilliantly! Though I didn't realise it at the time, looking back, it seems to me that doing the usual number of GCSEs at 16 would have been a very bad decision for my child. Not only is it likely to have wrecked their health, but it would have robbed them of the time to get really good at what they loved.
At no point did my kid say, "I'm never doing GCSEs." It was a case of "I'm not doing them this year. I can always do them later if I decide I need them."