There are many ways to prepare for exams. Some people like online programmes. Some use local tutors or tutor-led study groups where, say, half a dozen home ed teens might have a lesson together once a week. Some study on their own using textbooks. It is worth looking at all of these possibilities. A bright self-motivated learner might do well with any of these methods.
I don't know how critical cost is to you, but costs of doing exams independently can mount up. You need to pay a fee to the exam board and a fee to the exam centre where she sits her exams, as well as covering any costs associated with actually learning the material (books, tutors etc).
IF (and it's a big if!) the Local Authority accept that your daughter is too ill to attend school, you might get them to agree to a home learning package where they would cover these costs and your daughter could sit exams at school. In that case you should keep her on roll. But that isn't easy. It may or may not feel like a worthwhile route to pursue. Perhaps it would be wise to talk to local home educators to see whether anyone has managed to get your LA to agree this for their child.
If you deregister, then at an early stage you should identify an exam centre where your daughter can sit each exam. This is often said to be the most difficult part of getting a home educated teen through exams! Schools don't have to allow it, and most state schools can't be bothered. Some private schools will, and there are some separate exam centres. It's quite possible you will need to use various exam centres for the different subjects.
Most subjects are available as GCSEs or IGCSEs and there are several exam boards with which you can sit them. You need to find out which subjects and which exam boards are available at the exam centre(s) you will use, so your daughter can prepare the correct syllabus. I'm not familiar with Cloudlearn, but you wouldn't want to sign up for a course which follows (say) the English CIE syllabus only to discover that all your local exam centres only offer sittings of Edexcel English! Many people have made that mistake. This is another area where you would benefit from talking to local home educators.
On the plus side, through home education your daughter can have a wider choice of subjects and exam boards, and schedule them according to her needs. A popular approach is to do a few subjects one year, focusing on them intensively, sit the exam, then move on to different subjects the following year. Some subjects and some exam boards offer November or January sittings, which is another way to spread them out and take the pressure off - but be sure to check whether she's eligible to sit a certain exam in the winter; I believe some are only available as resits.
Here is a guide to get you started: he-exams.wikia.org/wiki/HE_Exams_Wiki