EDITED - to show fare is actually £1,290 with the code below
OK, so there is a snag. This is an ex-Athens fare.
However, once you've got to Athens (a Reward Saver redemption, of course!), it is all nice and easy. LOADS of availability at this fare (you need to return before 30 June) and you can get the A380 flights from DXB-SYD.
Actual fare inc taxes is Euro 1,717, so £1,423 at current exchange rate.
Given that BA's taxes on this route are c £730, it may be worth cancelling any booked Avios redemptions you may have and rebooking. On the A380's, the J seat is actually better than BA's (more leg room with the right seat, full bar at the back of the plane like Virgin has).
No idea how many EK miles this earns or how far you'd get with them, but presumably enough to at least do a one-way to DXB later from London.