The other question "My older brother has a fever", the correct answer is "我的哥哥发烧" - no 有. Why isn't it the same here? Like "你发烧吗？"
English usage permits the omission of the article, particularly when the degree of fever is not quantified.
Perhaps it depends on the dialect, but "do you have fever?" sounds unusual enough to my Australian English ears that if I were teaching, I'd correct it.
Manĝu terpomojn kaj feliĉiĝu!
Surprising that it's have in both languages, as a temperature isn't an object but a state.
I'd say that's because we treat it as a symptom or consequence of disease which we "acquire", so we "have" an upset stomach, a rash and a fever.
"Have you a fever" is a perfectly acceptable translation, DuoLingo still seems to have a fetish over "do you have..."