Hmmm- A little searching and I find that the McPeakes were indeed an Ulster Ireland family.
It is not clear at all, however, that Frank Mcpeake wrote "Wild Mountain Thyme," he was quoted as saying, in 1957, that it was a song that his father used to sing. I have the feeling that perhaps the song was handed down through the generations of singing McPeakes and the song naturally evolved from "Balquidder" to "Wild Mountain Thyme." Purely speculation, but a great illustration of the folk process at work, eh?