The name, Bridon, is likely also Brydon. For example, on 26JAN1837 Robert Brydon of Hodgdon, Aroostook Co., Maine m. Janet Carmont of Woodstock Parish.
If James and Agnes were still in Woodstock Parish in 1851 then they were the James Murphy b. Ireland ca. 1815, with a wife, 'Mrs. Murphy' (b. ca. 1825.) Their children were: John (ca. 1845), Julia (ca. 1849) and J. W. (1851.)
Another thing to consider is that Musquodoboit (if that is the place referred to) is in Nova Scotia. Outside of queries such as yours, 'Muskadabut' is not mentioned. Since Jeremiah's children were born in NS, I think you may be looking in the wrong place.
A relevant record may be that referred to at:
John Murphy & Margaret Jane Drysdale: Marriage records--Nova Scotia--Colchester--Indexes First Name John. Last Name Murphy Birthplace Woodstock (Carleton County) Residence Windsor (Hants County) Age 30. Status S. Occupation Farmer. Date1868-05-30. District 1 Windsor (Hants County). District 2 Colchester. Parents. James.Murphy. Nancy.Brydon. Spouse Margaret Jane Drysdale. Spouse Age 38. Spouse Status W. Spouse residence Tatamagouche (Colchester County). Spouse parents Alex Corby.Drysdale. Mary.X. Register Number 551.
Examining the record John Murphy did give himself as b. Woodstock, NB ca. 1838, the s/o James and Nancy (Brydon) Murphy. He would, then, appear to have been Jeremiah's brother. You may want to look at Nova Scotia more closely.