There is a joint birth and baptism registration in the parish where the child was baptized.The churches were the designated bodies to register births on behalf of the government.They kept two copies of the registries: one for the state (etat civil or vital statistics) and one for the church or diocese.Generally, you have to know in what parish where the child was baptized. Once you know this, you may through a Mormons (LDS) Family History center, order the applicable microfilm and make a copy of the record with the reader/photocopier. However, the LDS microfilming did not go beyond 1899. Some genealogical societies have the Drouin's microfilm that go up to 1945.
There is an of birth/baptism index for the Montreal area only but I would have to check the period.
Do you know in what parish she was baptized?
Once you know where she was baptized, there are two means of getting a copy of the record:
a. Drouin's microfilms and b. the Director of Vital Statistics for Québec (directeur de l'état civil). About $20.
I could probably help you with option "a" for a lesser cost.