Like C3, I have made this flight several times myself, but from the West Coast.
I find that flights from both LA and San Fran leave late at night local time, and arrive early morning local time.
I like to try to sleep from an hour or so after take off (they will usually feed you as soon as you’re high enough up anyway) as long as I can. This has worked for me because:
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It’s a 14-15 hour flight to Sydney, if I can sleep for 8 hours, that means I usually get to watch a movie after waking up, have breakfast, fill out my landing papers, and have only a hour or two left before landing.
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If I try to stay awake and then go to sleep toward the end of the flight, I find that sitting in the dark watching movies on headsets isn’t fun and makes the long flight seem longer, since I will have long periods of awakeness at either end.
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Hi…er…no.
Mistakes I have made include thinking that if I just stay up all night the night before, I will sleep most/all of the flight and it will be less…er…long and boring. In reality, this gave me “overtired child” syndrome at 36 years old. I was exhausted, wide awke, bouncy, over-emotional, cranky and stressed out, and the eventual crash hit I was on flight 2 of my 3 leg flight back to the US. I scared a flight attendant who (not knowing I’d come from overseas, I switched airlines) thought I was sick or drunk because she couldn’t easily wake me up to tell me we were landing.
Another mistake was not drinking enough water, you get really dehydrated.
I find the flight back to the US is worse, even though it is shorter (about 12 hours to LAX), because in general you tend to leave in the afternoon, Sydney local time. This means you are nowhere NEAR wanting to go to sleep and by the time you do go to sleep you are nearly landed and when you get there you’re exhausted. YMMV.
Dress comfortably, bring a toothbrush. It’s a LONG time without a shower. I second the recommendation to try to do some washing up. If nothing else, you’ll feel better and it will kill some time.
Try not to stare at the inflight map thing that tells you where you are, unless it is the last couple of hours. It makes the time go really slowly for me. Again, YMMV.
One thing I cannot stress enough is that when you are not sleeping you must get up and walk every hour or so when in the air. Deep Vein Thrombosis can lead to Pulmonary Embolism and that can kill you. I almost died last year from a saddle clot after a DVT (which, in fairness, was unrelated to air travel - or anything else that anybody can figure out, but I can say that they are a Thing To Be Avoided and will surely wreck your vacation.) Walk! Please!!
And hey, Sydney is fabulous, I love it! 
Cheers,
G