Proctor:
I suspect this your family. They had been in Canada for a while. There are lots of baptismal records and Lydia had atleast 12 siblings. Culleton surname (Any spelling) and the families of most of the daughters seem to have left New Brunswick by 1871. They are not in McAlpine's Directory.
Were the Burnett's Presbyterian. Lydia married in Catholic Church but all subsequent census records show them as Protestant.

Descendants of John Culleton

John Culleton b: 1797 in ireland or New Brunswick d: in of Dumfries, York, New Brunswick
..+Lydia Porl b: Abt. 1801 in New Brunswickd:
d. Aft. 1851 in of Dumfries, York, New Brunswick
m: Jul 26, 1818 in Fredericton, New Brunswick

Their children
..James Culleton b: Abt. 1826 in New Brunswick
..George Culleton b: Abt. 1828 in New Brunswick
..Michael Culleton b: Abt. 1830 in Dumfries, York, New Brunswick
...+Jane Meager b: in of Woodstock, Carlton, New Brunswick m: Dec 25, 1858
..Jane Culleton b: Abt. 1831 in New Brunswick
..Mary Culleton b: Abt. 1832 in New Brunswick
..Maria Culletonb: Abt. 1833 in New Brunswick
.......+William Helly
..Phoebe Culleton b: Abt. 1834 in New Brunswick
+John Harris m: 1864 in Fredericton, New Brunswick
..Margaret Culleton b: Abt. 1835 in New Brunswick
..William Culleton b: Abt. 1840 in New Brunswick
..Lydia Culleton b: Abt. 1842 in New Brunswick
d: Bet. 1869 - 1881 in of New Brunswick
.....+William John Burnett b: Mar 14, 1836 in NB m: Nov 02, 1865 in Dumfries, York, New Brunswick
...........3 James Wesley Burnett b: 1869 in New Brunswick married April
.........3 Bertha Burnett b: 1872 in New Brunswick
.........3 Charles Burnett b: 1866 in New Brunswick
...Hannah Culleton b: Abt. 1843 in New Brunswick
..Hetty Ann Culleton b: Abt. 1844 in New Brunswick +John Keafe m: Nov 15, 1865 in Fredericton,NB
..Rebecca Culleton b: Abt. 1847 in New Brunswick