How close in the Census was your Francis Doty living to either "Borders" or "Walls" surnamed families?
Sarah Doty married Jacob Borders and they moved into Sullivan County before 1840 when one of their older daughters (Berthena) married my ancestor, Dr. Nimrod Walls.
Sarah Doty was the daughter of Francis Doty and Sarah McKinney Doty.They were married in Rockbridge County, Virginia in 1788, Francis being born in New Jersey.(Check the original census; could it be "NJ" instead of "NH"?)
An early genealogy on the Doty family says that Francis and Sarah only had daughters.I think this is an error as the census listings do show minor males in the household.Your Francis Doty is most likely a younger son of Francis and Sarah or a grandson through a male child born soon after 1788.I have not done enough work on this family to tell you much more.
A brother or nephew of my Walls ancestor, "J.J." (Job Joshua)Walls" also left Sullivan County for Iowa.They might have moved as an extended family, which was often the case.