Those are perfectly good reasons to notate it with no sharps or flats in the key signature. That’s probably why whoever notated it did. But that doesn’t make it dorian. Those C#s give it away. No traditional tune in the dorian mode (either Irish or medieval) would have them. That’s strictly a D minor thing.
Apropos of nothing really, but..
Those C#'s make it D harmonic minor and I thought that traditional tunes were never in that dastardly modern German(?) invention.
Cecil Sharp[*] said:
"Personally, I have never recovered an English folk tune in the minor mode, and very few have been recorded by other collectors. Minor folk airs are, no doubt, Aeolian airs that have been modernised by the addition of a leading note."
Elsewhere he says that traditional English tunes do not modulate either (see P.59 of the same book) so this is probably a 'modern' tune or adaptation.
[*] See Page 60 of "The Folk Handbook" - you need to scroll down.