Didn't you have a camera works fine, but as you point out nobody says did not you have a camera.
You have not had a camera? is not the same question as Didn't you have a camera?. The first asks if the person has ever had a camera, and the second asks "(where is) the camera you used to (or I thought you used to) have".
So can the Portuguese sentence mean those two things ?
Duolingo, as far as I know, uses much the same set of translation pairs in the English from Portuguese course and possibly regards that as something too colloquial to teach English learners. Of course, there are occasions when it's the best choice (for expressing surprise for example) but accepting it may give the impression that literal translation works in all cases.