I can only recall the two airfields at Woomera. The main airfield near the town and Evetts Field both of which had bituminised runways. Evetts was adjacent to Range 'E'. Operated two-seater Meteors out of Evetts until 1970's. One of the pilots, Stan Borthwick was an ex-Royal Navy LCDR who I knew and told me the Meteors were used as radio controlled aircraft to teach pilots to fly the Jindivik from ground positions. He would go up as a safety pilot!
I believe the Royal Navy disposed of many Lend Lease aircraft at sea from off Brisbane and off Jervis Bay because many of the aircraft it operated in Australia from Mobile Naval Airbases (MONAB'S) were Avengers, Hellcats and Corsairs on Lend Lease Agreement from the US. More on the MONAB story can be found at:
The MONAB Story Home Page
Many secondary airfields in Australia became MONAB's e.g. RAAF Bankstown was handed over to the RN on 27th January 1945 and became HMS NABBERLEY. Whilst the RAN ended up operating three airfields as Naval Air Stations after WWII - Nowra, Jervis Bay and Schofields, the RN had many more in NSW and QLD during the latter stages of WWII. Jervis Bay still had WWII 'fighter' revements and buildings until the 1980's.
How long ago did you discover the Tiger Moths at Goolwa? I knew a pilot at Williamtown when I was there in the early 1970's bought a Tiger Moth at a cheaper price than you'd get a used car then. Think he bought it somewhere around Maitland.