The first thing to do, I would suggest, is to look up the distributions of the species, as shown here for Major Mitchell's Cockatoo:
The IUCN Red List of Threatened Species. Bear in mind there are 6 species of Rosella, some confiding, 4 species of Kangaroos (2 Wallaroos and about 30 Wallabies); Grey Kangaroo should turn up without too much difficulty. Rainbow Lorikeet may join you at cafes in State Botanic Gardens, always on the scrounge.
I would further suggest that the cockatoo, Gouldian Finch and Spinifex Pigeon are arid country specialists and can be elusive: Platypus has become locally extinct in more than a few areas, but I've met many people in Australia who have dipped on this species for years!; Koala in the wild has taken a considerable hit with last year's bush fires.
If you had been considering driving, a cursory look at some of the species' distributions needs to take in that Australia is vast and the last thing the authorities need is someone trying to cover 10,000km in a month!
Australian members of Bird Forum doubtless can give advice on how to maximise your chances for some of your species, but I think you'll find they'll be vocal in discouraging from confining yourself to a single vehicle! Many people use the internal flights to spend, say, a week in one area, renting a vehicle at each location, but remember that the wet season is November to April and travel in the north and from time to time in in the centre and in eastern Queensland roads are impassable.
MJB
