I am getting laminate flooring in a couple weeks, so I was very interested in ur question.
Two of the ladies in this group I belong to have it. So at our meeting tonight I asked them both about cleaning it.
One lady told me that she uses hot water, no soap at all. Gets the mop wet, & wrings it out as much as possible. Goes over the floor, it air dries, looks nice.
The other lady said she uses a gentle soap, nothing really strong. A damp mop, not very wet. It looks nice, too.
So the conclusion was, to wring the mop as dry as possible before going over ur floor.
I know what u mean about the desert dust. When I lived in Vegas, I could dust my furniture in the morning, & write my name in the dust on that same furniture in the afternoon.
I do not know whether that desert dust would make a difference in how u have to wash that floor. We r not in the desert here.