You can certainly make this trip happen. The best sand dunes are in an area clear across the country, almost near the border of Algeria at Erg Chebbi. There are lots of companies in Marrakech that will arrange transportation, over night stays, and a camel trek out to a Berber tent for a night of traditional music and food - in the middle of the Sahara.
My wife and I recently did this a month ago through a company called Morocco Excursions.
Its one of the few companies in the area owned and operated by local Berber and Nomads. We couldn't recommend it more and we were on time restrictions (I agree, to really enjoy its splendors, you'd need more time).
We did a three day, two night trip with Morocco Excursions. The first day was over the Atlas Mountains and into the Dades Valley Gorge for a night. The next morning we drove up to the Sahara, took the camels out at Erg Chebbi, slept in the Berber tent and then woke up the next morning for our drive back.
Quick trip? Yes. Doable. Definitely.
You can read my wife's blog for more details of our full Morocco trip (Morocco Excursion part starts about mid-way through). Hope it helps:
http://www.jaimefotheringham.com/min...wn-in-morocco/