To compete in hillclimbs and sprints you will need to be a member of a CAMS affiliated car club (you can search for your local Victorian club here: ) and a Level 2 S (speed) CAMS license. The CAMS license only requires a form to filled out, and generally speaking the club memberships and the CAMS license cost approximately $100 each per year.
Most clubs will be more than accommodating to new and inexperienced members, and will be happy to guide you through your first event. Just attend a few of their monthly meetings and you should be able to find out all the information you need.
Note: Most car club names are also due to legacy and misleading. For instance, you do not need to have a light car to be in the Ballarat Light Car Club (similarly with car club names that include marquees)