Darwin to Adelaide

I will be towing a camper and have a swag on board as well, so any camping/caravan/Roadhouse style camping willbe what I am looking for. Toilets would be referred and showers optional.

Will be only driving day light hours, but full days driving with a few breaks. Somewhere between 700 - 1000 kms per day, depending on the destination.

Safe places/towns are what I will be looking for as I will be on my own. Particularly interested in places to avoid.

I doubt that where ever you camp that you will be alone at that time of travel , although some of the more popular places will fill up by early afternoon.

With your stated preferences I would aim for:
Banka Banka - showers, toilets & grass camping.
Stuarts Well - free camp dirt area next to the roadhouse so toilets, showers and meals but does have a relatively noisy generator but we've tented there.
Glendambo - campground with toilets, showers and meals.
After that we're either in Cowell on Eyre Peninsula or Adelaide so can't help further on.
Honourable mentions are also Devils Marbles (fills early though), Kulgera, Marla roadhouse campground (quite average), Pimba aka Spuds Roadhouse.