You can see a dog walking beside An NPC I Hope you can keep one =]
There were dogs walking with NPC's in Oblivion and Fallout too, there's no indication that dogs will be pets.
Dog companion is the most cliche companion ever and I really don't want to see it in TES, especially considering the number of completely unique monsters walking around Tamriel that would make much more interesting pets.
Well...they are the most loyal and obedient animals, so there's no surprise that they'd be the first choice as an animal companion.