If you can I would suggest to get him to switch. I am left eye dominant and do everything right handed. I shot for about 10 years as a righty closing my left eye.
For the most part I did ok shooting like that. I ran into a few problems with the dominant eye trying to take over and screwing up some shots. As I got older and my eyesight changed I decided to switch and go lefty. It has been the best thing I've done. This has been my third year as a lefty and I am very happy. I now shoot with both eyes open and feel very comfortable. It takes practice to "get coordinated" but being a young kid it probably won't be too hard. In the long run your son will be happy.