Read through the above, although not entitled "Red is the Rose" by Robert Burns the lyrics used do come from a Burns poem. I am at work at the moment so cannot provide the reference.
Another one of Burns poems provides the bulk of the lyrics of "The Curragh of Kildare" I'll dig up the reference for that one and post back.
The above would date the lyrics at least to between 1774 and 1796.
As to the assumption that Burns only wrote in Doric Scots, please look a little closer at his songs and also his letters, particularly those to "Clarinda" they provide classic examples of english prose of that time. A lot of people tend to overlook the fact that for his time and circumstances Robert Burns was a very cultured and very well educated man.