Fiji Airways has a low fare of $596 round trip LAX to Sydney or Brisbane for departures on May 6 with other dates in May for $671, including flights to Melbourne. Expedia adds an additional discount and drops the price to $532 round trip for Los Angeles to Sydney departing May 6.
May 6 is the only date I see this fare on Google Flights.
There are a variety of dates for return flights depending on how long you want to stay in Australia. I even found an open jaw 15-day itinerary flying to Sydney and return from Brisbane for $533.
Fiji Airways Economy V earns 100% Alaska Airlines Mileage Plan miles. Round trip ticket earns 14,976 AS miles.
Fiji Airways LAX – Nadi, Fiji NAN – Sydney SYD – Nadi, Fiji NAN – LAX
Open Jaw Fly to Sydney, return from Brisbane
Fiji Airways LAX – Nadi, Fiji NAN – Sydney SYD / Brisbane BNE – Nadi, Fiji NAN – LAX