A lot of speculation on this song, but these are the basic facts, from Contemplator:
"The original words were an old ballad from Donegal which was collected in 1909. The words were "reworked" by Padraic Colum to this version. Alternate titles and variants include "Our Wedding Day" and "Out of the Window.""
http://www.contemplator.com/ireland/shemoved.html

The basic idea of the song is paralleled in other songs, some early, but no direct connection has been made to this particular song.

Mudcat has about a dozen threads on this song; picking the "meat" out of them is a slow and laborious task.