My daughter changed schools at that age. While we were still deciding where she was going to go, I included homeschooling amongst the wide range of possible options we were willing to support if it meant finding the right one. (She found it interesting to talk through how it could work as she's assumed it wouldn't be appropriate; did a bit of research; then stuck to her guns and is on a bursary at a boarding school).
If it had been a real option, I'd have been happy for her to be doing some work at home on her own without me there, and spending some time in the local library independently, and that would have increased over time. So yes it shouldn't be necessary for your to give up work to make it work. My youngest is just 13 and equally, if we were looking at home educating it wouldn't be leaving him alone that would be an issue, more supervision and oversight of what he was covering.
It sounds like your daughter has a lot of clear ideas about what she wants to do. Why don't you sit down and talk through the whole thing in detail with her, from where the idea is coming from, how exactly it would work, what would happen at exam time, future plans, all the practical aspects. Then also explore other ways of achieving the things that she is looking for that are different to her current schooling.
Ultimately you are in charge, but it does sound like she is starting to be ready to be treated as a young adult and she may appreciate be taken seriously on this. Even though your answer may well have to be sorry, it is not a good option. You will be able to make your reasons clearer to her if so, too. Good luck!