In the UK 1871 census, Kate was aged 1. Living at North Tower Hamlets, Mile End Old Town with her parents and three older siblings.
Her parents and siblings emigrated on the ship "Queen of the Age" 1874, London to Auckland, New Zealand and Kate was not on board, therefore can assume she passed away prior to this date.
Sources
↑ "England and Wales Birth Registration Index, 1837-2008," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:2X7S-YYG : 1 October 2014), Kate Harrison, 1869; from "England & Wales Births, 1837-2006,"
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DNA Connections
It may be possible to confirm family relationships with Kate by comparing test results with other carriers of her ancestors' 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 Kate: