Isn't this what Virgin Australia does with SIA? They basically codeshare with SIA and Silk Air on every flight throughout Asia. Difference though is VA started with nothing and are trying to grow by being a virtual airline.
QF actually was a real airline 15 years ago flying to more than Singapore, LAX, London. Really, QF's network outside South West Pacific in a year will be:
Singapore (45 flights a week)
Jakarta daily from SYD
Manila daily from SYD
Shanghai daily from SYD
Tokyo daily from SYD and MEL
London daily from SYD and MEL
Bangkok daily from SYD
LAX - from SYD MEL BNE
DFW - daily from SYD
Dubai - daily from SYD and MEL
Santiago - 3 weekly from SYD
JFK - daily from LAX connecting from SYD/MEL/BNE
Johannesburg: Daily from SYD
Hong Kong: Daily from MEL, SYD BNE, 3 weekly from PER
That's 13 destinations outside Australia, New Zealand and the Pacific. If you don't live in Sydney or Melbourne, Qantas can basically take you to Singapore and if you're lucky, Hong Kong.
I'm sceptical Perth-Hong Kong and ADL-SIN will stay for much longer. I'm almost positive PERSIN will be single daily in a year's time.
Who could cover Asia for QF? Maybe MAS? Their network is not nearly as big as SQ's though. But then they'll have a dual hub in SIN and KUL. The dual SIN DXB hub is already going to cause lots of problems with split flows of traffic because the SIN flights are really going to feed no where.