Just some of the destinations people I know and myself would fly to on QF should the option be available to (and I am based in Sydney - must be 100x worse for Melbourne and Brisbane, and obviously infinitely worse for Adelaide/Perth);
INTERNATIONAL
Beijing (easier to just fly CX via HKG)
Guangzhou (QF codeshare available, but often much more expensive than CZ)
Anywhere in China other than Shanghai (better to connect on CX via HKG than MU via PVG)
Anywhere in Japan other than Tokyo
Seoul (Can use QF codeshare, but CX/JL is superior)
San Francisco (QF is lucky here, most I know will go via LAX over flying UA)
Frankfurt (EK flight time doesn't work, arrives 9am. Now CX/SQ preferred)
Paris (Same as above).
Anywhere in India (QF/9W codeshare is rubbish with status benefits not honoured, and often more expensive)
DOMESTIC
Gold Coast (too few flights compared to VA/JQ)
Cairns (no evening flight anymore, unlike VA and JQ)
Uluru (no QF)
Most of the list above could be fixed quite easily, if QF invested in EK style partnerships with airlines such as CX and 9W