The people at The Session.org now have the tune in ABC and Gif form. Here's the ABC:

X: 1
T: Maid With The Bonny Brown Hair, The
M: 6/8
L: 1/8
R: jig
K: Dmaj
|:AG|FGE DA,B,|CD2-D2 E|FGA GED|=C3-CAG|
FGE DA,B,|CD2-DDE|FGA EDD|D3 zAG|
FGA BGG|=cA2-A2G|FGA GED|=C3-CAG|
FGE DA,B,|CD2-DDE|FGA EDD|D3 z:|

Here's the GIF of the dots