Hello from Australia!!!
Nice that you are coming for a discovery but I must say, 1 month is very tight to see so much from Australia.
I guess you will make a city tour in Brisbane up to Mount Coot-tha where you can see great views of Brisbane. Furthermore, Moreton Island / Bay and Koala Sanctuary are also some of the best highlights.
In Melbourne, you definitely have to go to Philip Island to see the penguins and you can also spend a day at Great Ocean Road to see the apostles. Those are the most important attractions.
Taking a bus to Melbourne from Sydney would be an idea but I personally don't like any kind of bus in the world. I would rather fly but if you feel comfortable in a bus, then it is ok. Just you shouldn't consider driving the complete way by yourself within a day because that's really tiring.
You need at least 2 days in Perth. One for a city tour which you can easily do on foot and another day on Rottnest Island (
Ready for Australia: Perth). If you have more time, there are really beautiful beaches close tot he city as well. If you have one more day, you can go to Fremantle as well. There are great places to the south of Perth. Margaret River region is famous of its wines. Esperance is the place where you can see sunbathing kangaroos on the beach if you are lucky. You can make a circle from Perth to the south to Margaret River, Albany, Esperance, and then back to the north to Hyden (to see Wave Rock) and then back to Perth. If you rush you need just a few days for this otherwise a week.
I hope this helps. Please do not hesitate to ask if you have any more questions.
Have fun!!
Mine