Yes, you can use Qantas points to book reward tickets on partner airlines, British Airways among them. The BA partnership offers both Classic Flight Rewards, where you use points to cover the entire fare, and Points Plus Pay, where you use points to get a discounted fare. This is covered in the "Use Points" section of the QFF website.
As with all frequent flyer redemptions, you book the flight through the airline whose miles/points you will be using, in this case Qantas. Right on the Book-a-Trip screen, you should see the options for booking:
You can also ask Qantas for assistance with booking over the phone, but this incurs an additional 35 AUD fee.
Reward tickets are not always easy to get. BA will only offer as rewards the seats it does not think it can sell. It may set aside reward seats for its own members before making them available to partners. As such, you may need to do a bit of hunting for dates and times where seats are available. Make use of the "Flexible with dates" option if you are in fact flexible.
As a further word of caution, BA is notorious for fees and carrier charges, not least on reward seats for partners. Sometimes, the "free" ticket is actualyl a terrible deal.