Thanks, everyone, for the input!
I had translated it just as you have suggested, go_Habs_go, but the basic underlying concept behind the German phrasing was bothering me and I wanted to make sure I got it right, so I wanted to ask the Forum users.
I think the problem with dust and eyes is that eyes are moist and cannot physically be dusty. Furthermore, dust cannot settle on them because they are usually either covered by the eyelids or moving around looking at the world. Besides, it takes a while for dust to collect/settle, so in order to have "dusty" eyes, one would have to be dead or made of wax. :-)
About humans exiting coal mines or standing on dry fields... There, I think you CAN describe them as "covered with (coal) dust" because the human body is different from the eyes. Still, DUSTY is not a term I would use for a human, again, unless dead or waxen.
For the eyes specifically, I would say "I have dirt/dust in my eye(s)". This is a temporary state rather than an ongoing condition, so you cannot really modify the word EYES with a word like DUSTY. Blue or swollen, yes, but not dusty.