J.C.
I have a 4 year old son. My hubby and I went to the Grand Canyon about a year ago and my mother-in-law watched my son for us. We didn't do the train, but we did do a lot of walking around the rim and there are so many places that are not fenced or barricaded off. I am glad we went by ourselves b/c I would have been a nervous wreck and not enjoyed myself. However, I did see other families there with children and they seemed to be doing fine.
If you can wait and are looking to plan an overnight trip, you should look into the Polar Express train ride in Williams. It is a family tradition of ours. The train ride is about 90 minutes long and it is based on the movie and book. It caters to the little ones. It is in Williams and you could do both (polar express train ride and stop by the grand canyon for a look see). The polar express starts in November and runs through mid-January. They have a hotel too and have a lot of fun childrens' activities. They run a package deal - for 4 people it runs about $300 for an overnight stay at their hotel, train ride, breakfast, dinner and $20 gift certificate to be used in their gift shop. You can't beat it. We love it. It would be a great memory or start of a new tradition:) The website is www.thetrain.com
Good luck:) Hope that helps:) Welcome to ARIZONA:)
Jenn