I don't think there's a such thing as a really cheap way to get to SYD. Especially on such short notice - the cheapest you'll be able to find will be minimum 2 grand most likely. Check award availability if you've got the miles. You may be able to do a LAX-BKK and a BKK-SYD ticket for a little less than a LAX-SYD - saving a couple of hundred bucks.