I changed my booking from Premium economy to business last year during a business class sale - Using the website. I cancelled my premium economy booking allowing qantas to keep the money. Then I booked the business class booking - just paying the difference. This way there was no cancellation fee and no change fee. Maybe I was just lucky.
I did try to do it with the call centre before I did it online and it took about an hour and was going to cost me - more for the flights as well as a fee (can't remember if it was a change fee or cancellation fee or both).