11. Under the Airspace Act 2007, CASA is responsible for determining when and how these classifications are to be deployed in Australian-administered airspace. CASA is to publish any changes to the classification of a volume of airspace and corresponding information through the Federal Register of Legislation (FRL) and then through the Australian AIP in a timely and accurate manner.
12. Pursuant to regulations made under section 11 of the Airspace Act 2007, CASA is responsible for the classification and designation of all Australian-administered airspace.
13. CASA has sole responsibility for the regulation of the design of all Australian-administered airspace.
This is from Australian Airspace Policy Statement 2018.
Seems pretty clear to me. CASA are responsible for determining the airspace at or away from an aerodrome.