Why couldnt the pony talk? Because he was a little horse.
But seriously, we dont know how the brain makes us laugh. But we can say that there are two kinds of laughter.
Complex social laughter is the kind that requires a sense of humor to get it. The other kind of laughter is in response to physical stimulation like tickling.
There is little evidence for a sense of humor in animals because animals can't tell us what they're thinking. But its pretty clear that at least some animals are capable of the second kind of laughter.
Chimps often vocalize something close to human laughter when tickled or chased. Rats chirp during rough and tumble play and when tickled. And dogs pant in a special laughing way that gets other dogs to chill out and make them want to play.