By Miss_Lynx?
A "mythic dog" could be any kind of dog that occurs in a mythical or folkloric context. There are quite a lot of them, across many different cultures — certainly in Celtic folklore, I've seen a lot of examples. One terms that tends to be used as a bit of a catch-all there is Cu Sith (Scots) or Cu Sidhe (Irish) — literally, hound of the fairies (the second word is pronounced shee in both cases). Basically, fairy dogs or otherworldly dogs. There are a lot of sub-types, but that would be a generic term for them.
See also