first of all , sorry about happened to your wife.It does happen around the world but Qatar is particularly bad. I always believe this country can bring out the worse in people sometimes.

i think it was more of your race rather than gender ( although that does influence the behaviour as well ).

you will find that Qatar will frustrate you on many levels, you either go insane or you will adapt. It will build character believe it or not, and yes its harder for women here regardless of whether they are on their own or not

maybe for the taxi( assuming its karwa) its worth asking how much before getting in( imagine you are on holiday, so use caution as you would then ).
if your wife can, go back when finished with video and see if she gets her money back, but keep a few steps away. so if they mess her about you can be witness and then step in by asking them how much etc and then challenging them if its incorrect.

you will find race an issue here in this wild west town !.
I can give you an example whereby I'm a Brit ( white English ) yet my wife is from Asia. Unfortunately people assume she is a Filipino or Indonesian maid etc ( not that I consider them any less a human being entitled to good manners) and look down their nose at her, despite the fact she is a major league lawyer and a graduate of oxford and kings. They get a shock when she can show up their lousy skills and abilities (especially the westerners and people originating from this general region). It’s one of the reasons we are selling up and leaving the backward mentality that exist here).

Both of you hang on in there. We have all been there, done that and got the t-shirt. Read QL, talk to your friends and you will both adapt and come out of Qatar shaking your heads in disbelief/laughter at this circus.
Regards