Several possibilities, unfortunately. One family that LOOKS to be a good possibility would be if her parents were Samuel and Ann ROBB, found in Northfield Parish, Sunbury Co, NB in 1871 Census, as follows:
Samuel, 46, b. Ireland?, Presb, farmer
Ann, 49, b. Ireland?, Presb (same for rest)
James, 22, b. NB
John Robert, 20, b. NB
Samuel, 17, b. NB
Margret Ann, 14, b. NB
She was already married to William by then, so not listed in same household. It's PURELY an educated guess, based on what information I can find. Here's the marriage license information on William and Rebecca:
"William Dykeman of the Parish of Northfield in the County of Sunbury and Rebecca ROBB of the same place were married by license this the twenty eighth day of September one thousand eight undred and sixty five, by me, J. W. Saunders, Baptist Minister."
This marriage was filed and registered April 24th 1866.
No parents are listed, however.
The fact that the were OF Northfield Parish in 1865, surely offers possible relationship, if not her direct family, to the Samuel and Ann group.
Samuel appears to have died in Northfield, on 10 or 15-Sep-1878, so is not listed in 1881, nor could I find Ann in that year.
Problem DOES exist on how old Samuel was when he died, as the record indicates 64 or 65 years of age, which would put his birth year closer to 1815 than the 1825 suggested by the 1871 Census.
Again, this is PURELY a guess based on location and age information known. I could find no listing of this family in the NBGS First Families indexes, either. Nor were they listed in 1851 Canada Census that I CAN access, as Sunbury and Queens are not all that well-represented in the database I COULD access.
Suggest having someone with access to 1861 Census for Sunbury County, and possibley Queens Co, do a look-up on ROBB families for you.