C.C.
I'm so sorry about your dog! Our cat Cocoa passed away when our older daughter was 3. I explained to her that our cat had become very, very, very old and had died. And that meant that Cocoa would not be living with us any more.
That simple explanation seemed to satisfy her and she didn't ask any further questions. What really amazed me was that recently someone had a box of kittens at her school, and the smallest one looked right at us and gave us a big hiss (Cocoa's trademark), and my daughter said, "Mommy! Cocoa came back to us in a new body!" I was absolutely blown away and have no idea where she came up with that idea, but I'll tell you what - we adopted the kitten! And she does have many of the same personality traits as Cocoa. Go figure.
Anyhow, my thought is to give your son the bare facts and let him make his own sense of it. He will make peace with it in his own way.
Again I'm so sorry for your loss.