I just recall that you also need to get a paasport for the baby. They need this information to issue the landing paper to the baby. Certainly a passport is needed when your family goes to Canada.
So get a passport for the baby first, then send a copy of the passport, original birth certificate, which shows the relation between you and the baby, fee, and a letter to processing center.
A lot of post offices provide passport service. You can find one close to you from internet. All you need is original birth certificate, photo, fee, and filling an application form, I think. Post office web page should have a required document list.