The Shaw family arrived in New York on 6 July 1866 via the ship Arkwright.  The ship manifest shows her name as "Jemima Shaw."

Although only Jane is listed on the overland company records, as head of household, the notation that she purchased 2 1/2 adult food rations indicates that the rest of the family was with her for this part of the journey as well.

She is the daughter of Helen Ann.  Her birth date is confirmed by the record in the family Bible, which appears with her the FamilySearch record of her brother Charles.  In this record, her given name is shown as "Jamina."  

[See https://www.familysearch.org/tree/person/memories/KL62-145]