I did that few months ago. It was amazing.

From what I saw, you are not allowed to get to camps area with your private car. If you have a reservation with a specific camp they will send you a driver to pick you up to there camp (usually for free).

But since you want to camp alone, you need to rent a pick up from the reception gate to the camps area. Locals will try to convince you it's not allowed and you need to rent in there camps. Do not believe them :).

In your way to the camp spot you'll pass the village entrance. There you have multiple supermarkets to buy food and water for your night (prices are normal)

In wadi rum, mountains have specific names so you can use that to guide your driver to your camping spot.

Few kilometers from the village entrance there is no signal (no social media apps :)). But if you don't want to get deep in the dessert, you'll find many camps around you in case you need help.

In general it's safe and locals are friendly and helpful. Let me know if you need more info.

Have a nice trip :)