They told us that Bebe was on only child, that she had to be bottle fed, and that that's what causes this behavior. She does it when she's tired.
We've had a cat or two that did this, but Beebers is the first dog.
Our Spook does the kneading and nursing, too. Since he was found along the highway, we have no idea why he does it, but it's soothing for him. He's almost 5 now, so I don't imagine it's something that's going to stop.