My first thought was that it was Em - Bm - Em but I agree with you it's D when played. I reckon it's in standard tuning as well but might be wrong.

I tell you one strange thing though - looking at the words definitely suggested it was going to be that sort of a tune. It reminded me of Cruel Sister in content of verses and various other things which have the Am - G - Em family of chords so it was amusing to find it actually sounded a bit like that!

It's also a little bit like a favourite song of the moment called Strong Winds for Autumn by Bob McNeill which I heard Emily Smith sing recetly and really liked (sorry - thread drifting)