If you plan to sleep on the second leg (BKK/SIN - SYD), go via BKK. The extra 2 hrs will make all the difference to your ability to actually sleep (instead of a 3 hr sleep between dinner and breakfast).
QF or BA has been discussed many times on this Board. It depends on how tall you are and whether you like short flat beds or long slightly sloping beds.
QF cabin service is better than BA.