The Empty Quarter encompasses UAE as visitors past Moreeb Dune, Liwa etc will attest.Maybe you're thinking of KSA, no empty quarter in the UAE and the way they're building there will be no desert left in Dubai soon either.
In all my time in Dubai I never heard or met any locals who even owned a dog, never mind hunt with them. Falcons and other raptors, yes they loved those. They would hire a whole plane so they could fly with them.
Rub' al Khali - Wikipedia