Think that the following link may be of interest ... it's from the National Library of Australia and traces the origins of Waltzing Matilda (and have copies of the old music)
The key words are
"The song came into being as part of the after-dinner musical entertainment at Dagworth. Based on musical and documentary evidence, the tune which Christina Macpherson heard played by the band at the Warrnambool steeplechase was almost certainly the Scottish song ‘Thou Bonnie Wood of Craigielea’. Robert Tannahill wrote the words in 1805 and in 1818 James Barr set them to music—music that, in turn, was possibly based on the old melody of ‘Go to the Devil and Shake Yourself’ . Thomas Bulch arranged James Barr’s effort for brass band in 1893 with the alternate spelling, ‘Craigielee’. There is also speculation about the relationship it bears to ‘The Bold Fusilier’, a song dated, in some sources, back to the eighteenth century."
So whether it's about stealing sheep / a Scottish Wood / the devil / a bold soldier ... ... or perhaps is even older. However our use of the title "Woods of Craigielea" and claiming it as a 200 year old Scottish song has more merit than using the more popular Australian title :>