Two things made me report this sentence: firstly, my answer should be accepted, "the cook asks where the waiter is" and the "correct solution" should, in case my answer isn't accepted, be equipped with, at the very least, a comma after main sentence. I might be wrong, but that's my humble opinion.
Look carefully at what I wrote; "the cook asks where the waiter is" with the correct word order, namely, the noun in the subordinate clause preceding the verb. This was rejected in spite of that this is what a native speaker would say and not "the cook asks where is the waiter", that sounds a bit non-native to me. Any native speakers of English out there willing to verify my theory?
At the top of this comments page (at least for me), where it says the initial question, it says "translation: the cook asks where is the waiter." So it would seem that Duo does accept your answer. Although DanFendel is definitely right that it's not a perfectly grammatically correct sentence in english...
I think the answer to your question is that, in this case, the direct object of asks is a subordinate clause and as such the direct object isn't "the waiter" but rather "the waiter is". את is only needed before a noun used as a direct object. I'm not a native speaker. This is just supposition from my knowledge of grammar.