You are too optimistic. There is no birth register in Quebec that is public. No problem prior to 1800 but no such register since.
Even if you knew the name of the parish in Montreal where the child was baptized, digitized records of the parishes are available till 1942 only.
You might want to post your query on the Montreal forum of Genforum. L'Islet is a county about 250 miles East of Montreal.