The period at which your ancestors left Ireland certainly is mostly associated with Protestant incomer migration. That is to say descendants of English, Welsh & Scots who came to Ireland in the 1600s, and who were not happy with various aspects of life in Ireland and so moved on again in significant numbers starting around 1718. In contrast, native Irish didn’t start emigrating in large numbers till the 1800s driven then by a population explosion, lack of employment opportunities, and various periods of famine.
However the name Quigley isn’t particularly associated with Scots incomers. You can use this site to see where the name was found in Ireland in the mid 1800s. Interestingly the surname appears to mean “an unkempt person.” https://www.johngrenham.com/findasurname.php?surname=Quigley
Looking at the 1901 Irish census there were 3601 people named Quigley. 3108 were RC but that does leave 507 who were Protestant. The name is heavily clustered around the Inishowen peninsula in Donegal and that’s an area known to have been settled by Scots in the 1400s and 1500s (mostly from the Western Isles, I have read). However they would have been RC, as Presbyterianism hadn’t made it to the Western Isles at that time.
I’d take the DNA ethnicity analysis with a pinch of salt. Mostly harmless entertainment. There has been so much internal migration around the British Isles in the past 2000 years as to make a DNA breakdown between Irish, Welsh, Scots, English etc pretty meaningless. Most of the population all share a common Brythonic origin (ie they are descended from people who migrated north through France as the last ice age retreated). So most of the population of Ireland shares common DNA with people in England and Wales. That’s because many of them are descendants of people who moved from England to Ireland starting around 6000 years ago. Trying to draw a distinction between the two is therefore is dodgy science. At the closest point it’s 13 miles from Ireland to Scotland. If I stand on the north coast of Co Antrim, on a good day I can see the distilleries on the Scottish island of Islay 25 miles away. (They have helpfully been painted white). It’s so close. Waves of people have been going back and forth between Scotland & Ireland since the end of the last ice age. It was an invasion of Scotland by the Scotiae tribe from Antrim in 495AD that gave Scotland it’s name. The genes and DNA of the peoples of Ireland and Scotland must be so closely related no scientific test can really determine separate ethnicity. (DNA is good for lots of other aspects of ancestry though).
