First I should let you know the correct name for the city is "Saint John" as opposed to St. John's, Newfoundland.
I found the family in the 1851 census of Saint John,NB.(actually 1852) Kings and Sydney wards.
HAYES Michael M Head 56 Irish labourer 1836 Mary F Wife 50 Irish 1836 John M Son 20 Irish labourer 1836 Julia F Dau 10 Birth Margaret F Dau 6 Birth
There was no Michael HAYES listed even when I searched for one born 10 years either way. Annie must have been born later in 1852 after the census was taken. I highly recommend contacting the following... The Diocese of Saint John Archives, for Roman Catholic Church records is located at 1 Bayard Drive, Saint John , N.B. E2L3L5 Phone (506)653-6807. Hours are by appointment only and it operates on a part time basis . A small fee for mail inquiries ; but allow some time for replies as staff is limited. Lots of early records on microfilm . Also some records have been transcribed and arranged in Family Groups.