In the 1851 census Elizabeth and her brother Thomas were attending school in Bodmin and staying with a family named Dann.
Elizabeth married Phillip Ham and they also immigrated to New Zealand with her brother Thomas.
Sources
1841 census - "England and Wales Census, 1841," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MQB7-PVK : 30 October 2015), Elizabeth Stephens in household of Thomas Stephens, St Winnow, Cornwall, 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.
1851 census - "England and Wales Census, 1851," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:SG2G-TF6 : 24 July 2016), Elizabeth Stephens in household of Henry Dann, Bodmin, Cornwall, England; citing Bodmin, Cornwall, England, p. 19, from "1851 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing PRO HO 107, The National Archives of the UK, Kew, Surrey.
Emigration Record - "New Zealand, Archives New Zealand, Passenger Lists, 1839-1973," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:FSBJ-RZV : 8 August 2017), Elizabeth Ham, 01 Jul 1864; citing ship Amoor, Archives New Zealand, Wellington; FHL microfilm
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DNA Connections
It may be possible to confirm family relationships with Elizabeth by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Elizabeth: