The most direct airway/s between Brisbane & Perth route via Brisbane, Amberley, Leigh Creek, Kalgoorlie, Perth; some 1986 nm (3678 km).
To track via Adelaide the distance changes to approximately 2027 nm (3754 km) a difference of only 76 km, or just on 2%.
The prevailing upper level winds in Australia flow from west to east, at varying strengths (speed) and direction, depending on the seasons and weather systems. In nil wind the 76 km difference would take the average jet 6 minutes. But depending upon where the jetstreams are, moving north or south of the most direct track can reduce the adverse affect of the usual headwind when west bound. One would obviously sit in the jetstream when eastbound, turbulence permitting.
There is no longer a service Perth - Ayers Rock - Cairns or vice versa, it ceased almost two years ago. Though Jet* operate a direct Cairns - Perth return nightly, though there are rumours that this might not be for much longer.