Qantas surrendered the right to be considered a flag carrier a long time ago.
Qantas were gifted the bilateral slots, something that they held at privatisation.
Qantas also decided that in 2011, "subsidiaries" ought have access to them as well, applying to the International Air Services Commission to amend the rights to reflect their preference.
A privatised airline is just that. Flag of convenience is another thing and the Qantas share register show a whole lot of foreigners too, ..
Given Little Napoleon is up in arms about airport monopoly pricing, he will enthusiastically offer one to Virgin, all in the interests of competition.