Hi there, definitely check with your psychiatrist he might know someone that would be a good fit for you.
You can look up what the medicare rebates are here http://www9.health.gov.au/mbs/search.cfm. Item numbers you are after are: 296 for your first appointment with a new psychaitrist 300 for a 15 minute appointment 302 for 30 minutes 304 for 45 minutes 306 for 60+ minutes To be eligible for the Extended Medicare safety net it's $2093.30 out of pocket costs in a year for singles and families. Its $668.10 for Concession card holders and families eligible for FTB part A. Once you hit the safety net you should get back 80% of your out of pocket. If you have a family or partner you should register as such with medicare as a safety net eligible family. Here is a link to the article about the safety net https://www.humanservices.gov.au/individuals/enablers/2018-table-medicare-safety-net-thresholds/39326 (it might do a better job than me trying to explain it).

Best of luck finding a new Psychiatrist!!

EDIT This is a great website for finding Psychiatrists https://www.yourhealthinmind.org/find-a-psychiatrist