There are a few shops around Mut, but they don't do much beyond the Khan al Khalili-style reproductions of Pharaonic carvings and cheap T-shirts. In Qasr, however, there's a small store with local handicrafts located just inside the entrance to the Ethnographic Museum. The prices aren't bad, and considering the options, you could do a lot worse than to acquire your Dakhla souvenirs here.
Some years ago, a few local women set up a stall selling local woven goods near the entrance to the old town of Qasr. Though a bit ad hoc, it's still there. Asking prices tend to be outrageous, but can be brought down to merely high with a bit of bargaining. All things considered, you're still only paying LE28-LE55 ($5-$10/£2.60-£5.10) for genuine local goods, and the money's going directly into some low-income households.
At the other end of the oasis, the women around the tomb of Pasha Hindi in Bashendi have been selling local jewelry to visitors for several years, and on my most recent visit their wares included some locally made clothes and a neat handmade wooden lock that you can see not only in the Ethnographic Museum in Mut, but in use around the orchards and pens of the oasis.
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