A bit more information - Genealogylibrary has the 1850 census images for VT. I checked it, and the name to me looks like Juliet - not Jabette and age given was 14.
Noah Dow and Hannah Folsom were m. 1772 - so wouldn't have had a child in 1836. There were 2 Deborah Gilmans in Gilmanton so not sure if one of them was the wife of Benjamin. Possibly Folsom was a name connected with Deborah - since there were Folsoms in Gilmanton at the time.