I am not sure why Sydney and not the North of Australia is your destination, but if you are set on Sydney for some perverse reason, then check out VRBO Australia (Vacation Rentals By Owner - we have used them all thu the USA and Europe and they are great value). Fully equipped and very comfortable:
http://www.vrbo.com/vacation-rentals...south-wales#41
Hope you have a great time - then drive North!
Merv