Thank you, Mr. M.
That is as you said, I think.
As to the first one, I think like this.
His dog is a happiness. (a kind of happiness his dog is.)
As to the second sentence, why no article here? I think it is because eventhough it is the same predicate nominative as the one above, it is different from the above one because it is NOT saying it is a kind of beauty but rather this is expressing his feeling. This is what I think. Please tell me why there is no need for 'a' here? Sorry if I ask too many questions on this subject.
This is (no 'a' why??) real beauty.