A few suggestions of frequent flyer reasons for the difference but I can't imagine even QF believe their FF program is THAT good (which it's not). Morno, you'd get the QF FF points if you booked through EK and lodged your QF number but you wouldn't get the status points; the only way to get those is to book through QF (as Metro pointed out). However, $4100 is a LOT to pay for some status points and it would take a great many lounge visits to justify that money.
I've basically given up trying to use the points of any of the airlines. I did have a couple of successful attempts with QF but normally it was 'computer says no', even when I was talking to the 'personal assistants' in Platinum One. Singapore Airlines want about 500 trillion points, plus $$s just to waitlist you and, to be honest, we don't have enough EK or EY points to make much difference.
When this agreement first came into being I was trying to do the same thing as now. Initially I was going to use QF points but then I had it pointed out to me by the Missus that LHR-HEL-SIN-MEL-PER was not the best way to get her back from the UK, so I switched to paying for a normal ticket. Again, using exactly the same flights but with an '8' in front of it to make it QF, there was a $300 difference. The QF lady said they were in the process of re-alligning the prices so they would be the same and, as it was early days, I believed her. Time has passed and $300 has turned into $4100.....that's a different kind of 'aligning' to what I'd expect
I did have a sensible PM asking if I'd got the dollar types correct, as a mix up with AU$ and US$ could account for the difference and would be the type of cock-up I'd make but, no. I re-visited the EK website and checked that everything was in AU$ and the difference still remains.
I guess EK will be getting the business even though I'd rather buy Australian
Edited to add:
Curiouser and curiouser. I've just been looking at one of those cheap flights-type websites and the same flights as above come out as $7418 with EK and $7443 with QF. Obviously MUCH closer to each other than the original case but now one wonders how the QF flights are $4500 cheaper than if booked direct with QF. My brain hurts.