I think in the near future most of all DXB-Australia flights will be with A380 especially when this comes into effect:
Qantas en route to alliance with Emirates
Don't kwow much about the bilateral / demand Australia-New Zealand.
1st Dec DXB-SIN daily A380 instead of DXB-JNB
Emirates Shifts Planned Johannesburg Airbus A380 Service to Singapore from Dec 2012 | Airline Route – Worldwide Airline Route Updates