From my personal experience:
Classic reward booking- points back automatically and usually instantly or within a couple of days. Fees and taxes you have a 50:50 chance of getting those automatically after a few weeks and having to enter the call centre cycle from hell (see below)
Fully paid bookings, even those that Qantas has canceled- usually you get a "credit note" so there's no choice but enter the call centre cycle from hell to get your money back. I've done this over a dozen times over the past year or so and have a few 'tips' from this: Always, always write down the name/ time/ date of when and who you've spoken to when originally requesting the refund. The refund is literally never coming though automatically after the initially promised 8 weeks wait time so you will have to call again to follow up. What then usually happens is once you get someone in the AU or NZ call centre on the phone, they will apologise for the wait and call up the 'refund department' directly while you are waiting on hold (agree with others here that morning hours are more likely to route to AU/NZ and, also, hold times for your agent to call the 'refund department' seem to be shorter in the morning) and once confirmed, you will get your money within the next week. They always talk about an email confirming the refund but that only arrives in about 50% of cases and sometimes way before or days after the actual money arrives so don't fret about it.
Of course, if you end up in an overseas call centre, you might as well put the phone down and dial again because that money will never ever arrive without you calling again. Oh and most importantly- try and keep your sanity while listening several times to the super annoying call centre introduction menu, endless senseless advice to instead sort your stuff online and, lately, a way too long blurb about international travel resuming while you only finally in the end want your god%@n refund.
CX is perfectly correct in saying they can't touch the *ticket*. But they certainly can touch the flights in the reservation - they've already done it once, albeit 'automatically'. it then needs to go back to QF to process the new ticket... but the hard work is already done. In theory.
