Welcome to the forum
The chances of getting into a CP during Xmas/New Year is very unlikely and they usually only take week long bookings at that time of year (that's what we have found anyway).
I agree with Pauly about checking the ozcamps sites but anything remotely close to the beach that time of year is usually pretty full but you may be able to squeeze in somewhere.
That stretch of Aust coast is extremely popular at that time of year & I would book ahead rather than coming all that way and having nowhere to camp but the side of the road!!
We usually camp from 26/12 to 7/1 and stay in CP's, somewhere different each year(near water, usually a river) and have found we have to book by March at the latest as they fill up pretty quickly and we also have found that a lot of people book from one year to the next, ie on check out they book again for the same time the following year. If you are wanting to stay coastal or near water you are going to find that your only option if not booking ahead will be free camps and National & State parks.
The camps 5 book is also a good reference guide to have with you on the road to see what is available at the next stop if you are not booking ahead.http://www.campsaustraliawide.com/information.php?product=CAW5SBB4
Hope this helps a little.