I keep reading posts here by people compalining their doctor wrongly told them to contact a hospital to get vaccinated or using hot docs (a GP booking system), then complaining they cant find Pfizer appoints etc
The official site to check your eligiblity and then search for places near you taking bookings for your cohort is:
Use the healthdirect Service Finder to locate your nearest health services in any part of Australia, such as GPs, hospitals, dentists, psychologists, hospitals, optical, pathology, pharmacies and a wide range of others.
covid-vaccine.healthdirect.gov.au
The site lists the Commowealth Respiratory Clinincs, GP Practices and the state run Mass Vacination hubs (and will list pharmacies when added), and gives an indication of when next available appoitnment is. The state hubs and RCs can then be booked online using the links as can some of the GPs, whilst others require a call.
If you are in 1a or 1b or over 40 and havent yet locked in your shot, try using the official site. Provided you are willing to get the recommended vaccine i.e. AZ for over 60s or Pfizer for 40-59s you dont need a GP referral of any kind to book via the official site.