My understanding of the codeshare agreement between EK and QF was that if you have booked an EK ticket, then you will not earn any status credits towards QFF… Only points. I could be wrong here, but thats just what I have heard on the grape vine (and also from using the QF Calculator).
From what Marc has said, it sounds like it is an EK issued flight/ticket. Therefore, you would earn 0 status credit, and only points. As you are already a Platinum FF with QF, I would base my decision on:
Do I want to earn QFF points?
Do I want to build my Skywards points balance and earn some status with EK