Thanks for getting in touch with your enquiry. It is not generally the duty of an au pair to provide an education for a child and if you do undertake this task, you should negotiate on the other tasks you will be expected to perform. Do not allow yourself to become overburdened and completely exhausted by this experience.
I’m going to try to answer all your questions below, in chronological order.
First of all, you seem unclear about the basics and legality of home schooling, so I’ll try to clear up your enquiry here. A home schooling teacher does not have to be a qualified teacher, and home schoolers are not required to teach from National Curriculum. In fact, there are no legal guidelines that would explicitly prevent you from home schooling this child: the rules surrounding adults who are home tutoring a child state that the child must receive a full-time education that is suitable to their age, ability and aptitude – but there is no discussion of the nature of the educator’s background, or qualifications.
As such, you would be able to teach the child in the eyes of the law IF you are able to provide that suitable education. Whether you are able (and want) to do so will depend on your circumstances, and that of the child. If he or she is four years old and you have had a university education, you might feel able to do so. On the other hand, if she or he is at Sixth Form level and studying subjects in which you do not have an advanced education, you may not be suitably equipped to provide the level of education required by law.
It may be useful for you to contact home education support groups such as Education Otherwise or the Home Education Advisory Service (HEAS), both of which would be able to tell you more about the home schooling process and decide whether you are up to the challenge.
As to the second part of your question, about a minimum wage, again there is no statutory outline of a wage for a home schooler – most home schooling teachers tend to be a child’s parents. There is a National Minimum Wage in the UK, however, which may apply to your situation depending on the nature of your employment and your age. Find out more about that on the government’s website Direct Gov.