There isn't a central registry for BMD's in Canada, they are by province. If the family stayed in NB or if the ship was out of Saint John, there could be something in a newspaper. Do you know when the father James died and where? There could be an obituary that would list members of the family still living to help narrow your search.
This is the info that I found from Vital Statistics
marriage (as written on the document)
April 4, 1916
Frank Ernest Hopkins 21
Residence - St. John, NB
Birth - Middlesex, Eng
bachelor, loaborer, Church of England
Parents - William @ Belinda Hopkins
Louisa Bennetta Gosling, 18 yrs
Residence - St. John, NB
Birth - Cardiff, South Wales, Eng
spinster, Church of England
parents - James & jane Gosling
witnesses - Murray Dunham ? (hard to read), St. John, NB
Mrs. F. Braid, St. John, NB
married by J. B. Champion
licence # 7633
transcribed Sousa Bennetta Gosling
birth 1912/02/21
Harry William Angel
Saint John, NB
Parents - Albert Henry Angel
Edith Jane Gosling
address - 151 Metcalfe Street, St. John, NB
Physician - Doctor Pratt
Mrs. Harry Green
The address 151 Metcalfe St and the middle name Jane was the factor that this could be another sibling of Edgar.