Wait, you are saying that the ATAGI for COVID-19, which was set up directly under the Minister of Health as part of the Federal Department of Health to advise and adjucate on everything immunity and vaccination related, who has produced all the current stringent Australian Covid rules, is somehow NOT part of the federal government ?

They have litterally made the rules, and are sometimes delegated to adjudicate on specific cases.

Checking that would have taken you exactly 5 seconds. It's litterally on their web page header, but in their statutes as well.