It wont cost you anything through the public system except the wait. It depends on which hospital you plan on having it as to the length of wait. Where I work it is as little as 3-6months at the very most. Although bigger hospitals I imagine would have larger waiting lists. You might struggle to get a Dr to do it at your age although I do know others to have it done younger then yourself. They might suggest something like the implanon/IUD until your seen to be at an older age.