The Australian government is subsidising the flights, but you are able to book on Virgin Australia and Qantas for the outbound flights. Example, Qantas has a flight on 12 April Melbourne to London, with set price fare of $1,336 AUD.

Please share how your call with Qantas membership goes. Whilst they may not be making any public offers at this time, for elite members so close to their anniversary, there may be exceptions-- especially with your record.