For me the perfect way to get to New Zealand (in my case) is to go on the evening services departures to Hong Kong. These get to HKG around 16:00 hrs, or so, maybe a bit later. You arrive, you're in the hotel about an hour later, maybe a bite to eat, you crash out and have a great sleep, but you may wake up a bit early. You then take a flight from HKG to CHC (in my case) the next day time, so back to the airport for something like a 09:00 hrs service to SYD (in your case) and that gets you into SYD around 20:00 hrs. You will then bounce up like the Duracell bunny the next morning, at least in theory. It's import to go eastwards, not westwards to HKG. Ideally you would have 2 nights in HKG.

Now I've not checked QR's schedules to see if going via DOH is within the same timeframe or not, but to some extent you can simply chop this around with anything similar where departing LHR afternoon/ evening gets you around 16:00 hrs local, or thereabouts to any of the following: KUL / BKK / MNL / SIN / BWN / DPS / CGK (if desperate).