They're not cats (that's for sure) and they're not exactly dogs. But they are something cute, sensitive, friendly and while not demonstrated yet, no doubt very protective. Not sure which is Stockton and which is Moreton. Except for color and perhaps gender, they are two of the same species. While their position in Silver Adept's entourage seems to be that of pets, with mystics, you can never be sure, and you should never assume...
Observations
As mentioned in their personal data section, they have a domestic appearance as pembroke welsh corgis. This is assumed to be an illusion to hide their real mystical form. But what creates the visual deception? Is it done directly by Stockton and Moreton as perhaps a natural defense? Or is it part of an overall spell cast by the Silver Adept to conceal all things of a enchanted nature that dwell within her Victorian home? Perhaps the best clue favoring the later argument is a single line of dialog provided by the Silver Adept's executive assistant, Raitha McCann; "I work here, the house doesn't hide from me." This alludes perhaps to some kind of spell, hiding all the mystic aspects in and around the area from mundane onlookers.
Footnotes
Quoting creator Kurt Busiek, "I think we called them "llama-corgis" in the script..."