I believe there is a mix, which unsurprisingly - and typically QANTAS - results in inconsistent outcomes for customers.
The South African call centre - which answers when the local timezone centres are closed - is outsourced and has a shocking reputation for rude, incompetent staff.
There is a call centre based in the Philippines which is also outsourced but with a fairly competent staff if all you want to do is enable a voucher, make flight changes etc.
There remains some call centre staff based in Hobart. These used to be the first touch point for the Premium call lines and were inhouse, very knowledgeable, capable staff. Unfortunately for the WPs (and above) amongst us, QF recently revamped their IVR such that it became a lottery as to where Premiums were routed. When I queried my last call with the Philippines based CSR (call wait times had also gone the way of the masses too, so I knew something was amiss) I was offered the opportunity to have my call transferred to Hobart - I declined because I just wanted to action a voucher and didn't want to drop into another queue having waited for 25mins.
There used to also be a call centre based in New Zealand where the CSRs were pretty good, but I think that was an early victim of COVID (or may have been the cost-cutting just prior).
The advice used to be to Hang Up and Call Again (HUACA) if the CSR you encountered was not up-to-scratch but I don't think I'd provide that advice to anyone these days with the protracted wait-times.
Regards,
BD