If you are lucky, her notes would have been deposited in the Provincial Archives of New Brunswick or, more likely, in a museum in what is now Miramichi, Northumberland Co., NB. That there are notes is suggested by the New Brunswick Genealogical Society web site, "First Families", especially at:
NEWMAN: John H. Newman born c1734 in England, d. 2 Jul 1797, married Hannah Montgomery born c1749 in Maryland, USA, d. 21 Dec 1807: came to NB in 1783 as Loyalists: first settled at Kingsclear, then on the Miramichi in Northumberland County: only child mentioned was, David Newman born 21 Dec 1774 in USA, d. 16 Jan 1852 in Derby, Northumberland County, married Mary Sherwood d/o Stephen Sherwood of Miramichi. Source: MC80/2689 Miramichi Branch of the NBGS, Some first families of the Miramichi, 2 pages: see also MC216 Kathleen Willis Williston fonds, MS 1B5 Biographies and notes on early settlers written by Mrs. Williston in 1947, 2 pages: see entries for David and John Newman.
As I understand it, John M. Newman was David's son. It would seem that the Miramichi Branch of the NBGS may have a line on any work on the family, See: http://www.nbgs.ca/http://www.nbgs.ca/ An address is at: http://www.nbgs.ca/contact.htmlhttp://www.nbgs.ca/contact.html
Is there any specific information you seek? For example, you can find John's widow, father and family in 1851 at: