Are you under the Delta umbrella for zed agreements?
I'll take a look again (did some research about going to Beqa Lagoon) This is what I got from the hotel:

"Air Pacific has a non-stop flight from LAX to Nadi every day except Fridays.
It is a 10hour flight and leaves around 10pm and arrives in Fiji 5:30am + 2 days.
You cross the dateline, so you loose a day going to Fiji, but gain the day returning.
Flight departs Nadi around 10:30pm and arrives into LA around 1pm same day.
We could help with flight arrangements if you like or feel free to
contact Air Pacific reservations at 800-227-4446. Rate is about $900 + $282 taxes.
Qantas code shares with Air Pac and offers the same flights, but you will
still be on the Air Pacific aircraft, but they may have different pricing."

So, if you're Delta, we have zed with Qantas but not as Air Pac code share. That's about all I can find right now.