While it is difficult to get business or first class awards on Qantas, it is possible. Unfortunately flexibilty in travel dates helps.

Now that you book Qantas awards through the Partner Desk, I think the furthest in advance you can book dates is 330 days. If wrong, I'm sure missydarlin will correct me. So your November 2007 dates are still outside Alaska's computer range.

Have you looked at the Award Chart? Qantas business class awards require 110,000 miles each.
http://www.alaskaair.com/mileageplan...sAustralia.asp

Assuming you have the miles, call the Partner Desk as soon as an acceptable travel date comes into the 330 day range for your outbound flight. Repeat the process the first time an acceptable return date comes into range.

You probably shouldn't limit yourself to only Qantas. Also explore with the Partner Desk other airlines as well as other routings.

I'm curious about your bad British Airways experience. Was it a problem booking a business class award? The Alaska program doesn't have an upgrade for miles option for flights on its partners.