hi,
There very few records in Ireland that go back to 1799 - compulsory registration of Births did not begin until 1864 for Catholics, and c.1846 for other denominations.
I am not sure if there would be Church Baptism records going back that far - and you would need to know in which Parish they lived in to locate the right church.
However...
There are a few family trees on Ancestry that could match your Thomas BURKE.
These entries appear to be for the same Thomas BURKE, but there seems to be a dispute over where he was born...
Thomas Burke
Birth: Abt. 1799 - Kilkenny, Ireland
Death: 14 Mar 1886 - N.S (Nova Scotia)
Marriage: Antigonish, Nova Scotia
Spouse: Mary MacDonald
The couple had 9 children Dorothy, John, Mary, David, Margaret, William, Donald, Thomas, Helen.
Only the descendants of David b.c.1838 are recorded.
These are the 100 BURKE families living in Kilkenny c.1823.
http://titheapplotmentbooks.nationalarchives.ie/search/tab/results.jsp?…
There is another tree...
Thomas Burke
Birth: 1799 - Waterford, Ireland
Death: 14 Mar 1886 - Nova Scotia, Canada
Spouse: Mary Mor MacDonald
Father John BURKE.
Only the descendents of Thomas's son William BURKE 1840-1932 are listed.
Birth 1 Nov 1840 in Cape Mabou, Inverness Co., Nova Scotia, Canada
Death 29 Apr 1932 in Mabou Bheag - Little Mabou, Inverness Co., Nova Scotia
There is a third tree which records Thomas's wifes family details...
Mary Mor MacDonald
Birth 1807 in Charlottetown
Death 04 APR 1885
Thats all I have I am afraid...
Regards,
SEAN