Sixth form is the last 2 years of school - years 12 and 13. Most students study for 3 A levels for 2 years but some schools also offer the 2 year International Baccalaureate pathway (6 subjects). Both are equally acceptable for university. There are other pathways for 16+ education like BTEC but not all universities/courses will accept them.
The school year starts in September so your DD would start sixth form in September 2020. If you are moving here before that, it will be quite difficult for her to transfer as the 2 year GCSE teaching finishes at Easter with exams the next term, unless she starts preparing for the exams before you relocate.
I suggest you do the following:
Contact the SA Embassy here for advice on transferring between the school systems.
Work backwards and find out about Optometry degrees in the UK and find out what their entry requirements are. They will specify both the required subjects and grades for A-level/IB/BTEC exams at 18 but they will also have minimum GCSE exam (the exams taken at 16) subject and grade requirements. You will need to contact them to ask how they deal with students who have entered the UK education system post 16 and have not taken GCSEs.
Once you have an idea what your DD needs to study in the sixth form, you would need identify which schools and colleges are near to where you will be living (the local education authority can tell you). If you are considering private education, you can use an advisory service. You can look at league tables and OFSTED (school inspection) reports to get an idea of how good the school is. You would need to contact the schools and colleges to see what their sixth form entry requirements are for non UK students (normally it would be based on GCSE results) and if they offer the subjects/courses your DD wants to study.
I would also recommend that you get the GCSE syllabus for maths and the subjects your DD wants to study for A level/IB and make sure with her current school that she has covered the syllabus before she starts.
I don't know much about specific schools in Kent but if you head over to the secondary education board, someone will. It has a grammar school (selective admission) system.