Hi! Yes, people home educate for all sorts of reasons: unmet special needs, no nearby school, parental preference, unresolved bullying, wanting more time for sports/hobbies/performing, or just that their child isn't happy at school. There's no wrong reason.
How to start... In part that will depend how long you plan to be doing it. If you are home educating in the long term then you can afford to let your child learn things at any age and in any order they want, as they are ready. For example, both of my kids learned to read and write at a later age than school would have required. That didn't impair their education at all, because they had one-to-one attention and could learn through discussion, observation, hand-on activities, and me reading to them. But if you plan a return to school in the near future, you probably want to keep up the skills which are valued there, so your child won't struggle when she goes.
Even so, you don't have to be too focused on exactly matching the school curriculum. Many topics aren't covered at a standard age at school anyway and it's no big deal whether your child has done each topic, so long as she is learning overall. For instance, if she joins a private school when she's ten, maybe her classmates will have done the Romans already and she hasn't, or vice versa, but that wouldn't hold her back. Most HE parents who plan a return to school just ensure they are working on reading, writing, and maths and then do whatever else they like or whatever their child has an interest in.
One common piece of advice from home educators is that when you start, give your child a complete break from any adult-led "schoolwork" for a while, especially if she has been unhappy at school. Let her do whatever she enjoys while she recovers. Stressed and anxious people don't learn well. With this in mind, it follows that if you are fairly sure home ed is worth a try, there's no reason to delay. You don't have to have all your ducks in a row before sending in the letter of deregistration: just go for it and figure out the details later.
While your daughter is easing in to home education, you can take your time to start looking around at different resources and thinking what you might like to try. There are no rules about what you have to cover, so it really is up to you. Don't spend too much money just at first, in case you buy something which doesn't suit and then you feel stuck with it, which could sour the whole home ed experience. There are free and cheap trials of online programmes. Libraries and online video documentaries are useful. You may be able to borrow materials from other local HE families to see what you like. Go along to some home ed groups and chat with people about what they use. There's huge choice, so keep experimenting until it feels right. Unlike schools, you don't have to have a grand plan and stick with it. You can afford to take time to adapt to exactly what your daughter most needs and enjoys.
There's no risk of her being "left behind" as she might at school, so if you can't find a maths curriculum to suit her just at first, you can pause with that subject until you do. When she's engaged, she'll learn incredibly fast. You don't need anywhere near the six hours which might be expected at school. Relax, play, go out to interesting places.