Hello to a fellow Ontarian Katie! Although my daughter doesn't remember anything about Disney as a baby, she still loves looking at the pictures from so many years ago! Attractions have stroller storage areas, where you would drop your stroller off before the attraction and pick it up when you're done. I wouldn't leave anything of value in it, but have never had a problem. Be sure to clearly label your stroller, as they are often moved, and it will literally be a sea of strollers!
There is so much to do in all theme parks. Be sure to use the
Baby Care Centers located in each of the four theme parks if you need supplies or a quiet spot to relax with your son. There are lots you can enjoy with your baby, and this
link will enable you to check out the attractions your family will enjoy, personalizing it for you, indicating the thrill level, age etc.
Write back with any other questions Katie!