In the transcription of the 1861 census for Westmorland county, Parish of Shediac, you will find the following:
Thomas Dolon, male, age 31, native, G Labourer, Cath
Marey A. Dolon, female, wife, age 28, native, Bapt
James Dolon, male, son, age 4, native, Cath
John T. Dolon, male, son, age 1, native, Cath
There is also another family with the surname DOLIN (may be related):
James Dolin, male, age 24, native, Gen Servant, Cath
Elizabeth, wife, age 24, native, Cath
George, male, son, age. .6, native, Cath
Mary, female, mother, age 65, born Ireland, Living with Son, Cath
Catherine Scott, female, age 11, native, Servant, Cath
SOURCE: Kenneth Kanner, ed., "1861 Census, Westmorland County, New Brunswick" at page 383.
On the NB Provincial Archives website, there is a death record for Mary Dowling, age 84 of Shediac, born in Ireland, who died 16 Oct 1889 in Shediac of inflammation of the lungs.
Hope ths helps.