In my research of late I noted the Dornin name popping up in various places in Virginia documents. Seems clear that they came to Virginia in the late 1700's and early 1900's, and the Dornin name still shows up in later years. An 1860 slave census from Virginia lists a John H. Dornin as a slave owner.
Maybe if folks could check their research for any hits related to Virginia and post them it could bear fruit.
I found the 1840 Richmond Virginia Census for John Dornin, my ancestor, which shows him to be about 20, with a wife (ann agnew) around the same age, and a young daughter (Sarah). Clearly the irish were prominent in the south, as there were many Irish fighting for the Confederacy.