The Carse of Gowrie is in Perthshire, which is not North East Scotland.
I think you could be right with "The Lass Of Gowrie" being the tune sought. I did find this by "Googling" "Kate of Gowrie" :
"The Regimental Quick March of the 70th Regiment of Foot, a Regiment which in 1881 became the 2nd Battalion The East Surrey Regiment. The song was founded on an older ballad by William Reid of Glasgow, called 'Kate O'Gowrie'. The melody was known as 'Loch Eroch Side' and was taken from 'O'er Young to Marry Yet' in 1757. The actual song, 'The Lass O'Gowrie' was written by the once famous poetess and songwriter, Lady Carolina Nairne.
There is some more - here is the link :