Happy laps is your ticket to have a cruise around a track and Open Practice and sprints are your proper go as fast as you want days. There's other categories for racing but they generally want proper race prepped cars.
Welcome to QLD Mathew, sadly you'll find that SAUQld is mostly dead. There are a few facebook groups kicking around but very little in the way of organised club motorsport.
I've not heard anything about exemptions being changed but TMR would e the people to ask. I do however agree with Josh about waiting and saving till you're on your opens.