I have a similar issue flying WLG-AKL-SYD(NZ)-HBA(QF) . The sector SYD-HBA is under a NZ codeshare. Not unexpectedly, I cannot do anything with this such as seat assignment etc on the app/web.

As a QF Gold, will calling Qantas after ~T-80 allow them to make a seat assignment, or am I condemned to wait until check-in at WLG?
even then, at WLG (or AKL) I suspect AirNZ won't get me a seat. But could I go to the QF desk at WLG (or AKL) to get a seat assigned? Worst case is the QP in SYD I suppose.....

Edited to add: My AirNZ (*A) ff# is in the booking, which needs to remains the case, so that probably doesn't help things regards my QF status allowing seat assignment.