Being a born and bred Aussie, here is some more information in addition to Bill & Sue's excellent advice.
Australia is a BIG country - 6th largest in the world - and (if you exclude Alaksa) almost as large as mainland USA. Getting anywhere will take time - so make sure you factor in lots of transit time between destinations. Also, due to its size - the weather will be variable. Try to stay in the south during the summer months, and head north in winter (unless you like cool, rainy weather and/or draining humidity).
There are not a lot of people in Australia - only 20 million of us - so once you are away from the South East Corner - be prepared for lots of space, and not many humans. If you are travelling away from the coastal areas, be aware that petrol/gas stations may not be that frequent - so if you tank is anywhere near a third full or less - it's time to get a refill. Also, if you are driving in the rural parts of Australia - be cautious of kangaroos around sunset/early evening. They have no road sense whatsoever - and headlights daze them - which means their next jump might be right in front of your car! There have been many cars significantly damaged by hitting kangaroos - but what is worse - human fatalities caused by kangaroos going through windscreens at 80+kmph. My advice, reach your destination prior to sunset.
I am fortunate to have driven around the whole country (and the middle) - over 20,000km in case your wondering - so here are the best places in my humble opinion (in no order)
* Sydney - opera house, harbour bridge and that magnificent harbour.
* Great Barrier Reef - marine life, the reef, the sun - try to do in winter months.
* Northern Territory - another winter activity - Uluru (near Alice Springs) and Kakadu (near Darwin) are fantastic - also try Katherine Gorge and Devil's Marbles. This is what I call the 'real Australia' because what you find here, you are unlikely to find anywhere else.
* Great Ocean Road - south-west of Melbourne - great scenic landscape - best in summer.
* The North-West - need to be a bit patient/adventurous to head there - the Bungle Bungle ranges, the Kimberleys, the city of Broome - this is a very remote part of the country - visit it in winter. Further south is the famous Monkey Mia - where wild dolphins come into the beach to say 'hi' (or whatever word/sound dolphins use).
Could write more, but that is a good starter. Feel free to ask me further questions!
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