Further to a contribution by Malcolm Douglas on 14 July 2001 (09.18) to the thread "Tabor - Heather Down the Moor", stating that:
"Dan Miller's 'Bonny Bunch of Roses' gives two tunes titled 'Heather on the Moor', which are however unidentified",
I noticed incidentally that a Jacobite broadside ballad titled "Brigadier M'Intosh's Farewell to the Highlands", kept in the National Library of Scotland Broadside Collection and, judging by the topic, the 1715 Uprising, probably published in 1715-1716, has a characteristic burden that reminds of "Heather on the Moor", whilst the rest of the text scans one of the tunes pretty well:

Lyrics of the song "Heather on the Moor" :

Oh as roved out on a bright May morning
Calm and clear was the weather
I chanced to roam some miles from home
Among the beautiful blooming heather.
And it's heather on the moor.

Lyrics of "Brigadier McKintosh":

M'INTOSH is a Soldier brave,.
And of his Friends he took his Leave,.
Unto Northumberland he drew,.
And march'd along with a jovial Crew..
With a fa la la ra da ra da.

The broadside bears the mention "to an excellent new tune". If the tune referred to is one of the two "Heather on the Moor" tunes, it gives a hint at how old the song is.

Particulars (sequenced tune, sheet music, etc.) may be found on my site, at:
http://chrsouchon.free.fr/mcintosh.htm