I'd dare say it's the SA code on QF over SYD that allows the connection to NZ - the PER connections are non-existant westbound (18 hour overnight required) and very lengthy eastbound - 0920 arrival from JNB, 1900 departure to AKL.
That particular GRU-AKL routing is a shocker -
GRU-JNB 1825-0715
JNB-PER 1645-0920
PER-AKL 1906-0530 (43hours + thanks to the transit times)

A quicker way is probably GRU-JNB-SIN-AKL or even GRU-ORD-HNL-AKL. But if it were me, I'd be doing GRU-SCL on LX, then use LAN to PPT then NZ to AKL to at least get some Star mileage in.