I'm inclined to think that Emirates are correct on this one, and that you are not eligible to be picked up & driven to SYD for what is effectively a domestic-only sector operated by QF - even though the sector IS of course being used to connect you to an onward international flight operated by EK, and ticketed throughout by them.

There are some complex T&C's attached to the CD service (not least within Australia & NZ) and part of them are summarised in this grid chart. The way I interpret it is in line (I believe) with what you have been told by EK.

http://content.emirates.com/download...ligibility.pdf