Civil registration of births (and deaths and Catholic marriges) began in 1864 so there will be no birth certificates for William and Matilda.
1901 is the first complete census for Ireland.
Therefore, you do need to get the marriage certificate. It should list the fathers' names but not the mothers.
Before searching in Irish records you need to check all Canadian sources (death certificates, birth certificates of children, gravestones, etc.) for clue.