Hi Dave,
I don't know if you can access that Ancestry link or if you have found it on Family Search, but I think I've found her 1861 Census link. I've also included some other links that I've found, the last of which (the 1851 Census) I'm not sure is her but has the right name, birthplace (Hundleby, Lincolnshire), and estimated birthdate (the census has her as a servant for another family at age 17). Because of the character limit I'll list this last one in the comments.
*"England and Wales Census, 1861," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M7DY-756 : 11 December 2017), Emma Davey in household of William Davey, Lound, Suffolk, England; from "1861 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing PRO RG 9, The National Archives, Kew, Surrey.
*"England Births and Christenings, 1538-1975," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:J3Q1-238 : 11 February 2018, Emma Thomasin Sanderson, 29 Dec 1833); citing , index based upon data collected by the Genealogical Society of Utah, Salt Lake City; FHL microfilm 508,044.
*"England Births and Christenings, 1538-1975," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:N6C2-J21 : 10 February 2018, Emma Sanderson in entry for Francis Brunyee Pidd, ); citing item 1 p 11, index based upon data collected by the Genealogical Society of Utah, Salt Lake City; FHL microfilm 1,450,398.
*"England and Wales Census, 1841," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MQ15-DC5 : 13 December 2017), Emma Sanderson in household of Reuben Sanderson, Hundleby, Lincolnshire, England; from "1841 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing PRO HO 107, The National Archives, Kew, Surrey.
*"England and Wales Census, 1871", database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:KZLP-W5X : 11 December 2017), Emma Thomason Pidd in entry for George Pidd, 1871.
*"England, Lincolnshire, Parish Registers, 1538-1990," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:QL1P-776F : 16 March 2018), Emma Pidd in entry for Annie Sanderson Pidd, 03 Jul 1864; citing Baptism, 03 Jul 1864, Hundleby, Lincolnshire, England, United Kingdom, Lincolnshire Record Office, Lincoln; FHL microfilm 1,541,985.