I think the earliest known copy of Fanny Power is in the 1840 edition of Bunting (presumably transcribed in 1792, though) where it's in 6/8, in D, intended for the piano, and just called "Fanny Power", with no "Planxty" in the title (though many other tunes in the collection are called that). The collection is on IMSLP.

There are lots of articulation marks; Bunting was obviously keen to get it right. Apart from the key, it hasn't mutated much from that, people still play it in much the same way. I would bet Steve Shaw does too, despite his insistence on orality.

By 1840, waltzes were an established form in the British Isles, and it was standard to write them in 3/4. If Bunting had seen it as a waltz he'd have said so.