The Sources list a baptism record without details, and I don't have access to the Drouin collection. I think that would be the most reliable source.
The 1861 Quebec census listed in the Sources gives 1860.
"Québec, recensement, 1861," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:MM7N-GGV : 9 March 2018), Josephine Blauchette, Arthabaska, Arthabaska, Quebec, Canada; citing line number 46, p. 36; Library and Archives Canada film number C-1262, Archives Publiques, Ottawa (Board of Registration and Statistics. Public Archives, Ottawa); FHL microfilm 517,353.
The 1870 US Census, also in the Sources, gives 1860-61.
"United States Census, 1870," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MDST-WJK : 12 April 2016), Josephine Blanchard in household of Humphrey Blanchard, Massachusetts, United States; citing p. 42, family 249, NARA microfilm publication M593 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 552,108.
I'd say 1861 is unlikely, since she was alive for the 1861 census. It would be interesting to know the date the family was counted, but it doesn't show on the Family Search record. If her birth month was really July, and she was a year old, she was most likely born before 1861. July 1859 is possible, but only the one record has that year (I think). I'd go with 1860 as an estimate.