I'd always thought K-9 might be more like a Scottish Terrier! I'd never seen Doctor Who before Nine but discovered K-9. He reminded me (although I'm sure the oppsoite is true- he probably was the inspiration!) of the little wheeled toaster-bots on the Death Star in StarWars ANH! I like to imagine they're the cutest PaDDs ever!A rather random and silly observation...
If K-9 from "Doctor Who" were "upgraded" to have a truly android (uh, "canoid"?) exterior indistinguishable from that of a real dog, he would almost certainly have to be a Corgi. If nothing else, it would lead to some freakishly cool sequences, like something from "Ghost in the Shell", the "skin" and "fur" around his ears folding like umbrellas to reveal parabolic scanners, his "nose" detaching to extend upon a telescoping rod to "analyze" objects, his jaw hyper-extending so that a beam emitter can emerge to zap things, etc.