You might want to have a serious think about be weather, particularly in relation to who your passengers are. A non GA flying wife or girlfriend is not going to enjoy that trip at all. You would want to avoid flying during the heat which will kick up very early and you'd be looking at at least 8,000 ft agl to get anything that resembles smooth air.
Ayers Rock in December? - Lonely Planet travel forum
At that time of year consider heading south, Merimbula, Mallacoota, Lakes Entrance, Phillip Island that'll keep you away from the Qld coastal thunder stormies.