Our son did his first 1 mile at about that age. I don't know what the course is like at your race but at ours it was easy to bail at any point so we just went out and figured if it was too much we would just leave the course. If he is an active kid and, as the other posters said, can do some runs in the neighborhood with no problem, I would say give it a try with no expectations. If it is a really cold day, though, you might want to make sure you have a way for him to stay warm enough while you wait for the race to start. The long wait before the race can be the worst part. Try hand warmers or layers for him that you carry on your back for the race part.