The short answer
Many do, with a slower plan. Merzouga is about 8 hours 30 minutes of driving from Marrakech, so split it over two days each way, choose a comfortable camp with real beds and ensuite bathrooms, and think about the camel: mounting is the hard part for hips and knees. Agafay, about 40 minutes from the city, is the gentle alternative.
In more detail
The road is the biggest demand. The route crosses the Tizi n'Tichka pass at 2,260 m, with hairpins, and then runs through the pre-Saharan south. Breaking it with nights in Ouarzazate or the Dades means no day in the car runs too long, and a private car means stops whenever you want them.
At the dunes, choose the camp with care. Comfortable camps at Merzouga have proper beds and ensuite bathrooms, and the gap between a budget camp and a good one is enormous. Nights are cold: about 10 to 15°C in spring and autumn, and down to about 2 to 5°C in winter, so pack warm layers.
The camel ride from the road to camp at Erg Chebbi runs about 20 to 40 minutes. There is no age limit, but the camel kneels and rises sharply, which is hard on hips and knees. If that is a worry, ask if you can reach the camp another way.
If the full trip is too much, an Agafay camp gives the open desert, the sunset and the fire about 40 minutes from Marrakech. Tell us about any mobility needs and we will plan the gentlest version.