Given that your daughter wants this and she's self-motivated, it is very likely she will make a success of it. You and she would need to accept that in some ways home education will give her fewer opportunities than school, and in some ways home education will give her much better opportunities than school. It looks different. Here are some examples of differences:
She's likely to have to change syllabus for some or all of her subjects. Some GCSEs cannot be done by private candidates, and they sit the equivalent IGCSE instead, as do most kids at private schools. In some subjects like maths there is very little difference, and in other subjects it's quite different.
Unless she does exams at college (which would be free), you'll need to pay fees for her to sit them, on top of whatever you may pay for her to learn the material. You'll need to find one or more exam centres which take private candidates and can accommodate the particular subjects and exam boards she wants. Arranging that tends to be a headache, but you'll manage it. You may have to travel for it.
Through home ed there is a vast vast range of subjects to choose from, and in some cases such as English Language you can choose the exam spec which suits your child's strengths.
Home educated kids often spread GCSEs out and take them over several years. Unlike at school, there's no particular pressure to sit all exams in a single session, or to be finished with them at 16, so your daughter could take an extra year if she needs it. For several reasons, most home educated kids do fewer subjects than schoolchildren, usually just enough to get onto the college course they want, typically five or six. But of course, the point of education isn't just to acquire exam results, and typically they will also be learning subjects which they don't take exams in. For instance, one of my kids learned a foreign language without doing a qualification, and studied art independently to a high enough standard to gain admission to university based on portfolio alone.
Home ed is a more efficient learning model, so she'll have more time on her hands for hobbies, a part-time job, or to study subjects in more depth. Driving her own education is great preparation for university and the world of work. (Years ago, I worked in the admissions office of a university abroad. We actively sought out home educated kids, because their background meant they hit the ground running.)