According to the article:
Do you think this is true? Do dogs dream about chasing rabbits? If so, wouldn't that seem to indicate the capacity for constructing a model of the universe in a dog's mind-space? Recollection as well as recognition? And possibly even a model of self? Or is the dog merely experiencing dream-emotions that cause it to twitch and "run?" In other words, it might be experiencing the emotions that trigger action without experiencing the physical perceptions (seeing or smelling or hearing the rabbit) that normally trigger the emotions.'People often wonder whether dogs that seem to be running during sleep are dreaming of catching rabbits or suchlike,' says Dodman [professor of behavioral pharmacology and animal behavior].
'I think, from the above discussion that one can safely say they are.'
Or maybe dogs have a model of the universe in their subconscious, but lack the capacity (language, for example) to access it while awake. During sleep, the model universe "leaks" into their dreams. Which might indicate that dogs are bicameral, but without the capacity to "hear" the auditory commands that bicameral man experienced.