http://archives.gnb.ca/Archives/?culture=en-CAProvincial Archives of New Brunswick
Under the Search column
Wallace Hale's Early New Brunswick Probate 1785-1835
put in Hayter, John
Will for John Hayter with wife Mary
Will for Mary Hayter 1827-04-09
includes names of her children and Sarah married to John Mooney is one of them
Newspaper Vital Statistics - Daniel F. Johnson
go to H, then to Hayter and enter John or Mary
John Hayter, July 15, 1818
Est. John Hayter, Westfield,Kings Co., Admin Mary Hayter, Hugh Johnston 22 June
John Hayter, Jan 17, 1826
d. Saint John, Wednesday night, Mary Hayter, widow of late John Hayter, Kings Co., formerly of Woolwich, England, age 63
Index fo Land Petitions, Original Servies
John Hayter, 1785, Kings
John Hayter, 1805 Saint John - 12 names on Petition inclduing Andrew Ham and John Wiggins
Index to New Brunswick Land Grants
John Hayter, 1809
Grand Bay, Kings Co., 1809/07/25, 200 acres shared in common with John Guiggy, Andrew Ham and John Wiggins
Using the names on the wills, you may be able to find other information in the Newspaper Vital Stats.
I would say that this is definitely the parents of Sarah Hayter who married John Mooney.
Looks like your line may be
John Hayter and Mary Monk
John Mooney and Sarah Hayter
Thomas Edgar and Sarah Elizabeth Mooney
Hope this helps.
Val