I am going to put in a bit of a guess here based on some knowledge but happy to be corrected
(it's been that sort of month for me!)
JQ use a different booking platform and management system. A very much LCC centered platform with dedicated functionality.
QF OTOH use legacy amadeus with a lot of manual processing on top for any number of reasons. QF refunds are taking so long, I believe, because every single one has to be manually processed by a human by the far queue. and the agents are WFH and all the rest... so takes time with a huge volume
I imagine JQ's platform is much better at processing. It's probably a button push for them and all integrated much more easily.
One of the main reasons is, that codeshares aside, the vast majority of JQ bookings are done through THEIR portal on their system.... they have a much better control over the incomings and outgoings than the legacy of Amadeus (specially with the hodge podge way QF seems to implement things on the platform which is likely because of codt reduction rather than an issue with the GDS itself).
IMO