"Off She Goes" is undoubtably not native American. Here's a copy from a book of mixed Scots and Irish, and a very few English tunes (this apparently being Scots). There's an earlier Scots copy (1789), but I don't have it.
[Campbell gave a different one of this title in his 19th book, but this is the only one that lasted.]

X:1
T:Off She Goes
S:Wm. Campbell's 20th Book of Country Dances (c 1805)
Q:120
L:1/8
M:6/8
K:D
A|F2AG2B|ABcd3|F2AG2B|AFDE3|F2AG2B|ABcd2e|f2dg2f|edcd2||g|\
f/g/afd2f|e/f/gec2e|f/g/afd2f|edcd2g|f/g/afd2f|e/f/gec2e|\
~d2fa2f|gecd2|]