Hi Louise,
Home education is a very different model from school, and there's a huge variety of options for how you go about it. One key point in which it differs from school is that because it's one-to-one and the child goes at her own pace, you don't actually have to have all the details sorted in advance. You can figure it out as you go along, and make changes as you go. There's no such thing as "falling behind"; it isn't like school where the rest of the class moves on regardless of whether your child is ready to do so.
In fact, I would liken home ed more to parenting than to school. Suppose you decide that your child doesn't have enough basic DIY skills. Unless she'd already left home, you wouldn't think, "Oh no, I've blown it." You'd think, "Okay, time to teach her how to paint. She wants her room redecorated, so this is a good time for her to learn how to do that." Or if you think she is capable of more and hasn't had enough responsibility, you give it to her now by getting her to manage more of her own money, or encouraging her to get the bus to town, or suggesting she go to see the doctor without you there, or teaching her to plan and cook a family meal - whatever she is ready for.
It's the same with academic subjects. There's no deadline. Outside of school, it really doesn't matter whether they learn algebra at 8 or 12 or 16 or later.
And even if you do have some sort of deadline in mind (e.g. she wants to do GCSEs at 16 so she can get on her desired college course the following year), they can get through an astonishing amount of material when they are ready and focused and allowed to do it in their own way. For example, my eldest, who had never done any formal maths at all, covered the entire maths curriculum and sat the GCSE exam in the space of nine months, getting a good mark. By its nature, school is very inefficient from the point of view of the individual child. They have to sit through things they already understand, sit and be baffled and ashamed when things go over their head, be disengaged by subjects which don't interest them, wait for the teacher's attention or for disruptive classmates to settle down...
So if you think home ed is the way to go, there's no need to delay. The prospect of being forced into school is probably hanging over your daughter's head so much that she can think about little else. You can just take her out and have a break from formal learning for a while, then start exploring the options and experimenting to discover how your daughter learns best. Experienced home educators recommend this as a good way to start home ed. If that idea makes you really uncomfortable, you could still have a positive start without needing all the details in place. You could do some museum visits or project-based work, so for example if your daughter is really into 1960s fashion you can cover most of the school subjects through that topic.
Meanwhile, you might like to get together with other local home ed families for academic and social opportunities and to learn more about the ways other families home educate so you can get some ideas.
Good luck! I'm sure your daughter will soon feel much happier when she knows she doesn't have to go back to school.