No BSL in Aviano area as far as I know. Just the usual landlord rules like, "No Pitbulls" or "No dangerous dog breeds". Most places I've found have been okay with dogs of any breed.
Well on the BSL front... I imagine you'll still have the dog when you come back after this deployment.... if you'll still be military I'd keep that in mind.
Who bans a Corgi?! Wow that might be the funniest thing I've heard all day!