Not saying you "should" credit to QF, but you "could". Or to another ffp. As this is FT flying and not getting ff miles is heinous crime.

I note you have Emirates in your profile. Are you a member off the Emirates ffp? If you have Emirates points you can use on QF & JQ. But not for QF upgrades.

Great Circle Mapper
Would need to crunch the numbers to determine ff point earning with QF ffp or another ffp.
With QR AKL-DOH-CDG 9400 & 3000 QF points one way & some status credits.
With EK AKL-DXB-CDG 9400 & 4000 QF points one way & nil status credits.
QF award AKL-BNE economy one way 18,000 points plus some cash
Are better ffp's than QF, but limited by the airlines you earn on.

QF fly B737 & A330 NZ<---> Au. Not worth upgrading on B737 (Or NZ A320)
QF ffp has a $ joining fee, which is easy to avoid.
And Jetstar JQ is owned by QF