Your child is asking a very deep question! And, of course, the answer to him is that God laughs at stuff that's really funny.
As the old Yiddish rhyme goes: "Ah mentch tracht, und Gut lacht." This means, "Man plans, and God laughs."
More than just a stitch of folk wisdom, this idea is well based in classical sources. "The One who dwells in the Heavens laughs," wrote King David, regarding the Divine take on those who try to wipe out the Jewish People. God snickers at them" (Psalm 2).
The futility of anti-Semitic plans to wipe us out is – ultimately – funny. People make plans, but God "laughs" when He knows that these plans will never materialize.
Now, God's essence is beyond comprehension. We, the created, can't understand the Creator. Still, the Torah talks about God in ways we can relate to, such as "God's Hand," "God's mouth," even though God doesn't have a hand or mouth in the physical sense. So too, God does not laugh as we know it.
But you can't invent something if you don't know what it does. To invent the light bulb and gramophone, Thomas Edison needed to know what sight and sound were. Therefore, God, who created everything including our capacity for humor, certainly "knows" a good joke when He hears one.
