A month isn't too long to grieve for someone you love - especially someone who was part of your family since you were born.
Speaking as another person who cries at the Humane Society commercials (!), death is only one of many, many hard things in life. Your son needs someone who can help him understand and face them.
You don't mention whether you are a religious family or not, but let's say you are not. Even then you can assure your boy that Rufus didn't desert him. Tell him that it's very hard to say goodbye to someone you love, whether that someone is dying or moving across town - whether that someone has two feet or four. Living things live a certain amount of time - sometimes a long time, sometimes a very short time - and then they stop living. We can't control that. That's the way it is on this planet. But we take the best care we can of those we love while they're here - and the love we had for them is real, and it's all right to cry (although meltdowns at day care are not preferable).
It's also all right to draw pictures of Rufus or do other things that help to honor his memory. (Have you thought about helping him send his pennies to the Humane Society, or even to the vet's office, in memory of Rufus?)
Tell him that there may be other dogs who need his love now. And tell him that YOU plan to be there for him as long as he needs you. I imagine that's in the back of his mind, even though he may not have said anything about it.
I love that cute puppy commercial, but I must say that telling your son that Rufus became an "angel dog" didn't help him. It helped you. You felt that you were in a tight spot and wanted to get out of it. That's a thing that happens to all parents (it sure happened to me!); unhappily, however, it's still lying. I hope you'll ask him to forgive you.
P.S. Just read your update, and had to go find a handkerchief. That's such a hard thing! Cancer is nothing but nasty, and even doctors can't always tell about it, in people as well as in pets. Rufus died without you all, perhaps, but he was in a place and with a person that he loved. So you didn't abandon him, either! It just underscores that we do not have control over everything that happens. Let's ALL love our loved ones the best we can while we have the opportunity. (Time to wring out the hanky.)