This kind of rigid 'mask-like' veil is very particular to the emirates and qatar. But it can be found in bedouin populations of other countries. Oddly enough it is called a burqa' (with a ayn at the end). I presume this is where the afghan burka came from.

Really, I had no idea Bedu outside of the Emirati-Qatari zone wore those things. Where is is worn?

I've seen it in Saudi, but it is very rare. Also in yemen, kuwait.. I don't think it is worn outside of the peninsula though.
Nabati poetry (if you can call it that) is always going on about burga' wearers.

I saw photos of the kind of face masks that I think you're talking about in a book about Iran. The editors claimed that the tradition was particular to Southern Iran (the Arab gulf areas) and had come from the Portugese, who had traded in the area during the 1500s or thereabouts. I have no idea whether that's true, of course.

I've lived in Kuwait for 15 years and I've never seen any woman here wearing that. I've seen it in the UAE (though not much in Dubai) and I think in parts of Oman (areas close to the UAE). It's actually made of a sort of cardboard, and there are different designs that indicate what area or what family you're from. I also heard that it came from the Portuguese; there are some old Portuguese forts along the coast in that area.

"Burqa" is used in various places to mean different things. In Saudi, I think they refer to their face veil as a "burqa", too.

Anyway, I think Fatima's great; I'd love to meet her!

Came from the Portuguese? Not bloody likely I should think, unless someone thinks Portuguese dames were wearing ball masques of the 18th century around frontier ports of the 15 and 16th centuries.

I would lay good money on an old origin of these things.