Hi, there isn't a short answer to this question, as it very much depends what course she would study and where. Eg students at a private FE / HE college get no work entitlement, students at a publicly funded FE college get the ability to work ten hours a week, students at a university get 20 hours a week. The amount of money needed to qualify for a Tier 4 visa (aka a student visa) varies according to where the course is and how long it is. The course has to be full-time and at a college, school or university with a licence from the UK Border Agency to enrol international students. The easiest thing to do is read this website carefully -
http://www.ukba.homeoffice.gov.uk/visas ... -students/
On options for your au pair to stay here, it depends how she entered the UK in the first place. Eg if she is here as a visitor (which I guess she did, as you mention her "holiday" in your post) she has to go home to apply for a Tier 4 visa, but in this case she isn't allowed to be working at all at the moment and you could get in trouble for employing her illegally... If she entered through another route she may be able to switch into the Tier 4 route from within the UK - the web site above should be able to help work this out too. There isn't a legal magical route, I'm afraid!
Feel free to message me if you have any other queries along these lines
Hope this is helpful.