Why wouldn't it? The promotion indicates any QF marketed flight number worldwide. The booking agent (in this case, QF NZ) isn't really relevant. If you want to be concerned, it would be the fine print in the T&C: "Double Qantas Points may not be earned on some fare types and booking classes including Classic Flight Rewards and any flight with a QF flight number on the ticket which is not operated by Qantas including; Jetstar, Jetstar Asia, Valuair, Jetstar Japan, Jetstar Pacific and other partner airlines. See
Airline Earning Tables for details." - ("... and other partner airlines" bit) however I'd be pretty confident that QF codeshare on EK is fine, as they've always been fine for such promotions in the past.
Anyway you booked the flight you already were going to book so isn't that the main thing?