Agree with dddc on the crucial need to get sleep SIN/SYD to get into the Aussie time zone.
On outbound to Oz, I'd suggest you don't try to sleep all the way to Singapore - try to wake up a few hours before landing & get your brain busy. If possible get a window seat so that you can allow some daylight in & watch the Malaysian coast passing below. Reason being that you'll be arriving in SIN late afternoon and in order to convince your body to sleep again after a "day" that would otherwise last only as long as the SIN transit, you need to try to be a bit active. I'd suggest heading straight to the lounge showers before the rush, then having a walk around Singapore's excellent terminal (especially if you haven't been before), rather than just slumping into a lounge seat for the duration the stop.
On SIN/SYD, you'll get 3 or 4 hours sleep if you're lucky, but at least your body will think it's morning when you arrive. Oh, and don't sit in row 10 or anywhere near the galley as the chatter, trolley preparation and constant curtain swishing will keep you awake through the night.
On the return sector, try to stay awake SYD/SIN and for perhaps an hour or two after take off SIN/LHR.