The off season for flights this way is April May June when the weather is not at its best and doesn't coincide with UK scholl holidays.
Cathay, Malaysia, Air Asia X, Thai, Emirates, Qantas (BA only use as a codeshare), Korean, Etihad from March, New Zealand and United all fly here. Most with at least 2 flights a day. After such a long flight from the UK the via Sydney, or any other Australian gateway, is not recommended as a straight connection. Only Adelaide and Melbourne have the international and domestic departures from the same building - all other airports require a transfer.
The route via the US is longer as it generally involves 2 stops LAX/SFO and AKL/SYD with United and New Zealand although Qantas do have a direct LAX-MEL service (and also one via AKL).
My folks generally use a consolidator who generally works out cheaper than the web fares. The problem is January is peak season both for folks coming here from northern hemisphere as its summer but also for Aussies head o/s on their summer holidays - the airlines know this and bump up fares accordingly.
Good luck
Rob