First, make sure that you've got an idea of the scale of the country. Think of the whole of Europe, from Ireland in the west to Poland in the east, and from Finland in the north to Spain and Greece in the south. Then add on about half as much again. That's Australia! It's massive and you'll only be able to see a very small part of it in a month.
A possible route might be to fly into Brisbane and spend about a week in the Brisbane/Byron Bay area. Then spend the second week based around Sydney. Head to Adelaide for a day or two but allocate the rest of the third week to Alice Springs, Kata Tjuta National Park and Uluru. That leaves you the final week to spend around Perth/Freemantle. (Make sure that you take a trip out to the Red Desert, it's unforgettable).
If you wanted to add Melbourne to the list, you could squeeze it in between Sydney and Adelaide. (Alternatively, you could go via Hobart, Tasmania).
Chris