Driving up the gold coast does sound the dream indeed.
No it's horrible, don't bother with that at all if you've only got one month.
If you can, WA is the 'real' Australia. I drove round most of Aus and WA was by far the stand out area, the east coast was an anti climax after the west. Get to Perth and if you can, down to Margarets River and up to Ningaloo Reef, much more accessible than the barrier reef, just walk into the bath temperature water off the white sand beach and straight onto the reef, surrounded by amazing fish. Depending when you are there there are whales and manta rays and turtles and all sorts too. I loved Perth and having a beer at Cottesloe as the sun sets over the Indian ocean is a real treat.
Melbourne and Victoria in general are lovely. Great ocean road is a lovely drive.
Byron is amazing and inland from there is stunning. Fraser Island is pretty cool for a day or two.
Nullarbor is quite an experience to cross in a camper van, probably the most isolated I will ever be in my life.
Sydney, very scenic, its nice to get the ferries everywhere but it didn't appeal to me that much. Blue mountains are pretty but absolutely crawling with tourists.
To be honest, australian cities are just other cities where people speak english, drive on the left and drink beer and coffee, so I would make the emphasis on getting away from the cities. A month is long enough to see some amazing sights. I'm well jeal!