Biography

Julia Mary (Maria) Dickerson was born in 1815 to Dr. Aaron Dickerson and Mary Connaroe, a Philadelphia lady. They settled in Marcus Hook PA where Aaron was a doctor until his death in 1824. "Genealogies of Long Island" says that Julia was consequently brought up by her uncle Mahlon. This is confirmed by a 1850 census, where an 80-year-old "Mahlon Dickerson" lives with a 35-year-old "Julia M Dickerson" in Randolph, Morris, NJ. Julia may have been taking care of her aging uncle, who died and was buried nearby in Succasunna, NJ in 1853 (SOURCE 6). Julia didn't marry for the early part of her life but in 1852 was married to Joseph Van Atta(1809/24-1879), a man with five young children from another marriage (SOURCE 7).
Search process:
"Cousin Julia" was originally found in 18380314LCC_MJS1: "I had a letter from Julia Dickerson last week, she says she is coming down next week, to make us a good long visit... Cousin Julia is coming..." The obvious first conclusion was that this particular cousin is of MDC's maternal line. MDC's mother is Mary (Dickerson) Canfield, and Mary's only living siblings are brothers: Mahlon (1770-1853), Silas (1771-1807/61), John B. (1786-1822/76), Aaron (1781/3-1824/71), and Philemon (1788-1862). A search for the progeny of these brothers led to a "Julia Mary Dickerson" as found in SOURCE 1. 
Further search in the New Jersey Historical Society's Dickerson Manuscript Collection (SOURCE 3) turns up a married name, Vanatta, or Van Atta, and a death date of 1881.
However, sources disagree upon which of Mary (Dickerson) Canfield's brothers was Julia's father. The Ancestry source (SOURCE 1) and SOURCE 4 assume John B., but SOURCE 2 says Julia was the "daughter of Dr. Aaron Dickerson of Philadelphia." The Census record from 1850 says Julia Mary was born in Philadelphia, and SOURCE 5 corroborates that Aaron was Julia's father in Philadelphia.