if you have already headed to Noosa from Brisbane then you are not far from inskip point which is one of the best spots for Black-breasted button quail.
The best sights in south east queensland would be Lammington NP/O'Riliey's and Mt tamborine.
From Here down to Sydney I would head to the capertee valley to the west of Sydney and the Royal national park. You can do the Royal in a day but leave at least 2 days for the capertee. South of Sydney Barren grounds is worth a stop as long as the weather is good.
Heading south to Melbourne I'm not sure where to stop but there will be good birding on the way down, if you want to go the long way inland you could go via lake Cargelligo.
Once in Melbourne Weeribee is the best place to go, I don't know Melbourne that well but to the west of Weeribee you can see Rufous bristlebird at places like point addis.
Bare in mind Australia is a big place and there are a lot of long drive between the big cities, would you be able to take more than 13 for your trip?