OK, I've now seen the answer elsewhere - the indefinite article can be omitted in Danish for some items of clothing such as shirt or dress.
Do you know if it is for all clothing or just a few exception words?
Any item of clothes or shoes. "Har han skjorte/bukser/sko/hat/frakke på".
Why is it not "Har hun en skjorte pa"?
That would be Does she have a shirt on. Emphasizing she
Is it incorrect to say "har han EN skjorte på"?