Steve many tunes are performed differently by diferent performers, or by the same performer at different times. Indeed one the arts of the musician is to be able to adapt a tune for different dances. And as musicians we have the tools to describe how we are doing this; in this case time signatures, which we use to describe the basic flow of the tune.
Fanny is often played as a waltz in 3/4 time, but just as often rather slower, in 6/4 or even 12/8 (which sounds as though it should be fast, and can be; but isn't always - a piece from roughly the same period, Messiah_-_How_beautiful_are_the_feet; Score and here , sung by Joan Sutherland - although probably a little slower, has a similar rhythm).
How O'Carolan originally conceived it being played we shall never know.