Not all of the Canadian records are available on Ancestry, so I'll give you some links to direct resources, and a few thoughts that may help.
Here is the direct link to your 1861 Census record: https://www.bac-lac.gc.ca/eng/census/1861/Pages/item.aspx?itemid=182296
If this is the right family, they also appear in the 1851 Census: http://www.bac-lac.gc.ca/eng/census/1851/Pages/item.aspx?itemid=408833
It is a puzzle, because I don't see any records for any Doyles who settled in Northumberland in the NB Genealogical Society files online, or in the Provincial Archives (where you can find birth, death, cemetery, land records, and a useful newspaper index).
But I do see a couple of clues in the 1851 Census. First, it indicates the family was Catholic, so William's wife likely had more than one name. Its possible that she used her formal name for formal purposes, and gave the Census her everyday name. My own mother did that! Its also possible that Bridget died and he remarried.
Second, it indicates he and Bridget were both born in New Brunswick, which can rule out some Doyles who emigrated after he was born.
The earliest Doyles were in Restigouche, and he doesn't seem to be connected to them, either. They had a William much older, and another much younger, all accounted for.
Finally, in the 1851 Census, the Doyle family is living right next to the Flynn's, who may be related to William's wife, based on your information. I see beside them a Pickles family, and NBGS First Families shows a William Doyle (born in Sussex, the son of Hugh Doyle and Nancy Sheck), who married Sarah Pickle June 16, 1818. The Pickle/Bickel family were Loyalists from NJ. Please remember that I'm speculating here, and the listed source is simply an archival reference "MC1/Doyle", which is not available online. (Feel like a trip to NB?)
In Old North Esk, Hamilton notes a Francis Flynn who came to Northumberland and was contracted to work on some roads in 1821. He may be the one in the Census, but Hamilton doesn't give any information about Francis' family, so I can't tell if Bridget, or Helen or Nora could be related. But the son named Francis suggests it may be possible.
If you can access through your library, these books may provide clues for the Doyle, Flynn and Pickle/Bickel families:
That's all I can think of :)