With seeing a doctor we have two main systems that you can use and each will have a different waiting time. Bulk-billing and the fully public option has longer waiting times because there aren’t enough clinics/specialists or doctors, The reasons for this are complex but they stem from an unwillingness from prior governments to raise the amount the government pays for each service to adequately to support this system meaning less doctors and practices being willing to support it.

You’ve then got practices/specialists etc… that charge copays and they tend to have less waiting times because less people are willing to pay copays. A lot of these practices will also do outright private billing which is what you’re experiencing.