If you check the Singapore Airlines website you can often find good internet fares there. We've used these SIN-BKK. If the fare rules say :

KrisFlyer Accruable: Yes

(which they usually do) you will get UA miles at 100%.

http://www.singaporeair.com/sg

Not sure if the Australian prices are that good though. SIN-SYD R/T comes out $795 SGD + $117 SGD tax = $912 SGD or about $497 USD. SIN-BKK R/T is only $350 SGD.