by the looks of it you seem to be planning to drive all the time and not stop. The distances here are enormous and your plan Sydney - Cairns will take you the equivelant of New York to Miami. You will also be driving during the hotest part of the year which given the Australian sun could be a little overwhelming.
You are coming during the summer school holidays here and I would expect good hotels will need to be booked ahead. The motels along the way will be OK and will rnage from the good to the crappy, many will have vacancies. But its pot luck.
A better option might be to fly into Australia through Bribane, go to the sunshine coast from there, fly to Sydney from the Gold Coast and then motor to "Newcastle". (3 hours on the motorway sounds about right.
Back to Sydney for Australia day also sounds right, lots of events during the day followed by fireworks. If you can get a room at a hotel in Darling Harbor you will be right in the thick of it.
Hope that helps PM me if you need more
also check out
http://www.nsw.gov.au/Culture.asp
http://www.australia.com/home_US.aus...er=y&L=en&C=US