I am not sure how Elizabeth Fullerton is related to the Fullonton/Fullingtons that lived in Rockingham County NH and moved to Franklin, VT Here is what I found. James Fullerton b: 1800 New Hampshire married Sarah Bray. Sarah Bray was born 1804 in Massachusetts
Elizabeth Fullerton b: Feb 2, 1827 Brighton, Suffolk, MA
James and Sarah (Bray) Fullerton are living in Carroll County, New Hampshire on the 1850 Fed Census and in Belknap County, New Hampshire 1860, 1870.
The census' may help you locate your family memebers