As a descendant of John Hazen of Oromocto, and having done extensive research on the family, I believe she is not of that Hazen family.
John's son, John Hazen, had an illegitimate son, George Hazen, born Jan 29, 1842, who was known to the Hazen genealogy. but there is no mention of another child.
The illegitimate children of the sons of William Hazen of Saint John were all recognized and were named in their father's and grandmother's wills.
I have found these unidentified Hazens In the 1851 census
Sunbury County: Sarah Hazen, servant.
Hampton Parish: Anne Hazen, 18, from Ireland 1851, servant in household of Joshua Scribner, inn-keeper.
And this unidentified Hazen:
Date March 24 1830
Newspaper The New Brunswick Royal Gazette
"d. M. HAZEN, Monday morn, Lower side Hartt's Island opposite Springhill (York Co.) Sleigh broke through ice."