There's potentially an argument to be made that Prague's 'Africa Up Close' functions as a sort of desert house, if your definition of desert includes scrubland (and given the existence of the Kalahari it potentially should).
The main issue with defining it as that are the notably tropical species housed towards the right-hand entrance - tenrecs, jumping rats and bush babies. But dry forests are just a couple of trees away from a desert...right?
If the surrounding complex is included, there is also fennec fox and mongoose.
I think this is where defining where a desert starts and ends is quite difficult. The Zagros mountains are certainly dry to the point of arid, but equally contain greenery in scrubland and forest. I guess there's an argument to be made either way.