United Airlines have round trip airfares travelling from Los Angeles (LAX) to Singapore (SIN) for $599, nonstop. Or if you do not mind 1-2 stops for a few hours, then Xiamen Airlines have this for $482 round trip.
Travel Availability on UA $599
Departs LAX: Monday thru Thursday from Aug 22 thru Nov 29
Returns: wide and good availability returns
Travel Availability on Xiamen Airlines $482
Departs LAX: Oct 15-18, 20, 22-25, 27-28, 30; Nov 1, 4-8, 12-14, 19-23, 25-30; Dec 3
Returns: wide and good availability returns thru Dec 28
Use dates and book it on Orbitz [orbitz.com]
, Expedia [expedia.com]
or Travelocity [travelocity.com]
. Bundling hotel with airfare will save money. Two samples attached.