No Oneworld airline goes to Fiji, so a Oneworld award isn't possible. Qantas codeshares, but those flights aren't available on a Oneworld award.

As rrgg said, AA has what they term an all-airline award. You can use any combination of the carriers, but you would have to go from the US to Fiji via the south pacific and not via any other continent. So your options are to go BWI-DFW/ORD-HNL-NAN on AA and Air Pacific or BWI-DFW/ORD-HNL-SYD-NAN on AA, Qantas and Air Pacific.

I think you can book 330 days out, iirc. Judging from the posts on the AA forum, seats on Air Tahiti Nui and Air Pacific were always plentiful, but have gotten harder to book in the past year or so. Seats on Qantas are notoriously difficult. Seats on AA are hit and miss.