The place Katherine came from is probably Killyleagh. There is a parish called Killyleagh, and within that a village of the same name. Katherine might have come from either. There are several references to Morrison families in Killyleagh in the attached link:
There were 18 Morrisons living there in the 1901 census, all but one being Presbyterian, which would indicate they were originally Scots settlers, probably under the Hamilton & Montgomery settlement of Co Down & Antrim in 1606.
Killyleagh 1st Presbyterian Church has baptism & marriage records going back to 1693 (with some gaps). I’d be inclined to look in them for her baptism and family. These records have been copied and you can access a copy in PRONI, Belfast. (They are not on-line anywhere as far as I am aware).