I would recommend you doing the STAT. If you have done any previous study (such as Cert IV or Diplomas) that could improve your chances, as can work experience, even if unrelated.

There are alternative pathways for gaining entry such as writing an essay to back up your past experiences. Make sure if you do this you are careful to address the exact selection criteria and give specific examples.

Some courses you can apply straight to the uni. Others you must apply through your relevant authority such as QTAC in QLD, UAC in NSW, etc - check out their websites. Usually they provide guides for would be applicants, as will uni websites (try propective student links).

Hope this helps - also if you are planning on doing nursing, or teaching, perhaps contacting their professional association and asking questions could help.

BTW I know MANY MANY mature age students in varying disciplines. You probably have a good chance. You have life experience, something a 17 or 18 yr old is yet to have time to do, no matter how clever If you don't get in, keep trying - it will happen and you can make your dream come true.