Yes I believe the dogs do, but I haven't spent a lot of time dissecting this or being able to study it (maybe I can figure out something the next time I'm dogsitting for my cousin).

Here's the link... http://www.psychologytoday.com/blog/canine-corner/200911/do-dogs-laugh

Regarding the second idea, that would probably be something good to do. Look at animals (other than humans) with breath control and consistent physical similarity, who thus have similar social situations as early man where they needed to organize themselves without knowing already who was the worker or the leader, and thus predict that they'd have a form of laughter.

I haven't gone into the animal side of it too much yet, but I'll keep that in mind.