Does he have or has a dog?

Excuse me, I couldn't help but notice the slight inconsistency in your phrasing. Typically, when inquiring about someone's possession of a dog, we would use the present simple tense, "Does he have a dog?" rather than the present perfect tense, "Has he had a dog?" The latter implies a completed action in the past, which may not be the question you intended to ask. So, to clarify, are you wondering if this person currently owns a dog, or are you inquiring about their past ownership of a dog?