You can use this site to see where in Ireland the surname was common in the mid 1800s:
The vast majority of Grahams were in the counties of Ulster, and that’s because most arrived as part of the Plantation of Ireland. Many were moved here in the period 1610 – 1625 from the Scottish Borders because of trouble they had been creating there. (If you are interested in the background read The Border Reivers by Godfrey Watson. Plenty of cattle thieving, feuds and murders).
Thomas Graham is a very common name. In the 1901 census there were over 300 in Ireland and there would have been just as many in 1801. So without some idea of where the family lived it will be very difficult to trace your particular ancestor.