She is not listed in the widow's pension application, but she is 7 at the time of the census of 1860. It is logical that she died before July, 1863.
The Historical Records section of FamilySearch.org has a New Hampshire death record for Ann Bartlett. She was 9 Years and 9 months old when she died. The cause of death is listed as "throat distemp's" The death record does not list her parents' names.
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It may be possible to confirm family relationships with Ann 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 Ann: