Here are a few more suggestions.
The site I linked to copied the obit from
Daniel F Johnson's New Brunswick Newspaper Vital Statistics, which are hosted on the Provincial Archives of New Brunswick (PANB) website:
http://archives.gnb.ca/Search/NewspaperVitalStats/?culture=en-CAThe text of the obit should be here (his surname was spelled Frazer):
http://archives.gnb.ca/Search/NewspaperVitalStats/Details.aspx?culture=en-CA&guid=a9e7f355-7bb5-4396-9963-66c6b3ad4c56&r=1&ni=107398So the question is: was this his obit? If yes, then he was born in Inverness-shire.
The obit says he received a school license in 1823. The PANB website has an
Index to Petitions for Teachers' Licences & Payment 1812-1882 (RS655) here:
http://archives.gnb.ca/Search/RS655/?culture=en-CAThis is what the site says about the petitions:
"This series comprises petitions, certifications and copies of licenses. The extant records in this series are records of action when teachers asking for government licenses submitted petitions between 1812 and 1882. These documents contain biographical data such as names, country of birth, education, teaching experience, church affiliation and samples of handwriting. Local school trustees and clergymen attached certificates verifying the petitioner's teaching ability and his/her moral and religious character."
If you do a search on Donald Fraser, you'll get several hits for Northumberland County. You'd have to write to the PANB to request copies. Perhaps you might get lucky and find some useful information.
You could contact the The Miramichi Branch of The New Brunswick Genealogical Society and ask about sources of info:
http://www.nbgsmiramichi.org/index.htm . Perhaps they might have biographies or other indexes that might name your Donald Fraser and might provide clues.
According to this website, it appears that your Donald Fraser was listed twice in the 1851 census; have you seen both entries?
https://www.nbscottishhistory.ca/data-sources/1851-1861-census"Donald Fraser was counted in both Glenelg and Newcastle, Northumberland County in 1851. Being a teacher, Fraser was recorded both at home and where he was keeping school."
It might be worthwhile to write to any libraries in the areas, just in case he was mentioned in any local histories.
Regards,
Josephine