الترجمة:The dog is our dog.
In general, Duolingo wants you to be accurate in translating what the sentence says and not just what it means. "الكلب كلبنا" is most accurately translated as "The dog is our dog." Although your sentence carries the same general meaning, it's not an accurate translation.
But when translating "The dog is ours" to Arabic, the most common translation is "الكلب كلبنا". So I think it should be accepted.
that is the aim for this site, to make a literal translation.
the idea behind the whole website is to translate the web through the learners, sometimes they put some real sentences that they get from the web, as an exercise for the learner, and if 10 learners or so agreed on one translation, system post that translation for a translated website of that content, like wikipedia.