MacLysaght’s the Surnames of Ireland says Dallas is “A Scottish name established in Co. Derry. Dalhouse was an earlier form. Derivation (dweller at) the dalehouse.”
Huge numbers of Scots settled in Ulster in the 1600s, something like 200,000 of them. By the 1700s many were dissatisfied with life in Ireland and started moving on again, often to North America. Your family may well have been amongst them. In North America they tend to be known as Scotch-Irish and in Ireland as Ulster-Scots. Bit of history here:
https://www.ancestryireland.com/wp-content/uploads/2017/08/The_1718_Mig…
So the short answer as to your family’s origins may be that some generations were born in Ireland but if you go further back to the 1600s they probably originated in Scotland (where the name remains common).
Presbyterianism was established in Scotland in the 1550s and brought to Ireland by Scottish settlers, most of whom lived in the counties of Ulster. I don’t know when your ancestors left Ireland (you haven’t said) but if it was early 1800s or before, then many churches don’t have records for that period, and of the ones that do, they are often not on-line. So that may be why you cannot find any information.