It resembles the song "I care for nobody, no not I, and nobody cares for me" but it's not the same.

Does she really play it that low? I'd expect this:

X:1
T:Nicky Nack-Nack
S:from the playing of Sally Sloane
L:1/8
M:6/8
K:D
A|d2d (cBA)|f2f e2g|f2A  A2B |=c3 (cBA)|
  d2d (cBA)|f2f e2g|f2A (ABc)| d3- d2 :|
g|a2a  a2f |ggg g2g|f2A  A2B |=c3 (cBA)|
  d2d (cBA)|f2f e2g|f2A (ABc)| d3- d2 :|

I've cleaned up your notation a bit - no need for variant repeats if you make the repeat start on the upbeat.

Afterthought: I looked it up in Charles Gore's "Scottish Fiddle Tune Index", which gave me the "official" title.

X:2
T:The Miller of Dee
B:Sabine Baring Gould, 1895, Old English Songs from English Minstrelsie, 1895 
F: http://www.folkinfo.org/songs 
M:6/8
L:1/8
K:GMin
D     |G2G ^F2  D|B2B  A2c| B2 G A2^F|G3- G2 
w:There was a jol-ly mil-ler once Liv'd on the riv-er Dee, 
D     |G2G ^F2  D|B2B  A2c|(BA)G A2^F|G3- G2 
w:He work'd and sang from morn till night, No lark_ more blithe than he.
(B/c/)|d2d  d2  B|c2c  c2A| B2 G c2 B|(B3 A2) 
w:And_ this the bur-den of his song For-ev-er us'd to be,_
 D    |G2G ^F>=ED|B2B HA2c| B>AG A2^F|G3- G2|] 
w: I care for no-bod-y, no not I, If no-bod-y cares for me.

England's new national anthem.