OK, I think I figured it out.
I added some sources to Jeanette's profile a couple weeks ago but had another look at it tonight.
Her death record gave her parents' names as David Gilmore and Mary Hunter.
The 1910 Census indicates she immigrated in 1891, so she had to be captured in the 1871 Canadian Census.
The 1871 Census of Chinguacousy, Peel, Ontario, shows ''Jannet'' with David and Mary Gilmore.
Looking at birth records, there is a James Hunter Gilmore, born 5 Mar 1874 in Chinguacousy, Peel, Ontario, to David Gilmore and Mary Hunter. Also David, born 28 October 1871.
Finally, looking in the Wesleyan Methodist Baptismal Register, there is a Jennet Keening Gilmor, born to David and Mary Gilmor, born in Toronto Township, born 20 Sept 1868, and her brother David, born in Chingacousy, born 20 Oct 1871, both baptized 24 December 1871, in Chingacousy.