United Airlines has cheap Australia flights from $649 to $670 round trip for nonstop flights from Los Angeles and San Francisco to Sydney, Australia for departures from December 2018 through September 2019.
There are plenty of summer 2019 dates available in June, late July and August at $649 to $670 round trip for nonstop travel June to August with United Airlines.
From LAX, there are also similar prices with Delta/Virgin Australia.
In fact, there are many cities around Australia priced around $650-$700 round trip with Virgin Australia like Melbourne $637, Brisbane $653, Cairns $674 and Hobart, Tasmania for $706.
United Airlines San Francisco SFO – Sydney SYD – San Francisco SFO
Virgin Australia Los Angeles LAX – Melbourne MEL – Hobart, Tasmania HBA – MEL – LAX