I think it should absolutely be accepted. The beauty of language is that different nuances are conveyed in different sentence structures. "The dog of his is black" sounds more poetic, or semantically chosen for a specific context, or for stylistic reasons. Perhaps the distinction isn't the same in Portuguese, but some distinctions are. To be fluent in a language, one must learn different manners of usage, and be able to distinguish one from the other. By allowing people to translate this sentence either way, duolingo would encourage this. That would be good for encouraging people to think creatively and critically about sentence contruction, which, as I mentioned above, is vital to fluency.
Of course, that is with the assumption that one wants to be fluent, and is using duolingo as a primer.
Yes, I think it should be accepted, but I think that it is important to remember that Portuguese fluency is the goal here and the literal translation is often not a good translation since this Portuguese version is commonly used while the English literal translation is rarely used.