Wow! I went to school in Canada in the 60's (also late 50's)
as a child and this song sounds so familiar to me. I even came across an old book of children's rhymes (from Canada) but could not find that song.
Seems like he (the little boy)did get hit by a car and he was ok but I do not recall how the verses went.
I think there were more verses like you said and I wish I could remember them. Did go to the thread menioned by Susan of DT but did not know any of the songs on that thread.
I hope someone will know this song you are trying to track down as I am curious myself now.
Ha, maybe Joni Mitchell knows of it. She went to school as a child in Canada but not in Ontario, although that song might have been taught to children in all the provinces and territories of Canada.