It's not a huge deal, but we won't need the facilities provided by a caravan park; caravan parks may

Is it possible to park a fully-contained campervan, i.e. with own loo and shower, anywhere in these areas? Or must we park in a caravan park? We wouldn't mind driving out of the town limits a wee way if necessary.
It's not a huge deal, but we won't need the facilities provided by a caravan park; caravan parks may be crowded at a time we may prefer solitude; and caravan parks cost extra (albeit not much, granted, but it's a small factor in the equation).
I am just wondering why you would pull over by the road, but i am hoping you are not rear ended or side swiped or hit by a another car, bus or truck in your darkened campervan enjoying your solitude while you sleep.
There are also publications available that list free camping spots around Australia and also plenty of websites (search free camping Australia and numerous sites pop up). Here is just one that looks like there are some in the area you want:
Ha - tonight I saw a classic! We're having a little film festival at the moment, with films showing in the town hall. There, parked in the car park is a small camper van (think wicked or similar), with a station wagon parked next to it and they're obviously setting up camp for the night. Two hours later, car rentals at fort lauderdale airport after the film has finished, there they are, with a large council wheelie bin dragged across to their cars, small gas burner sitting on top, cooking their dinner!
We rely on using the Free Camping Guides that are available in larger newsagents as well as asking others that we meet. I don't agree about seeing Australia camped up with Semi Trailers at road side stops but the free option car rentals at fort lauderdale airport if you are self sufficient does have an appeal.