You mean as in: "I can't believe he is doing this!!!"? If that is what you mean, than no, not necessarily. You can use that word order in the sense of "what is he doing?" and in the sense of "he is doing what?", but for this last sense to work you'd really have to stress the last word (as you do in English). Check out the discussion I had with Davu just above.
I'm sure you use "quê" when it's a noun, like in: Ela tem um quê de mistério = She has a touch of mystery.
But about this case, I've been reading, and found texts stating the same as Davu has shown. When que is at the end of the sentence, even if it's not a noun, it receives the accent because it becomes "tonic".
Com acento circunflexo:
--- Substantivo masculino: Seu olhar tem um quê de misterioso e vago.
--- Interjeição: Quê! isso é intriga.
--- Pronome em fim de frase:
Fumar pra quê? / Ele falou não sei o quê / Analise como e por quê.
(que) With circunflex accent:
--- Masculine noun: His/Her look has a touch of the mysterious and of the vague.
--- Interjection: What! This is intrigue.
--- Pronoun at the end of phrases:
Smoke for what? / He spoke I don't know what. / Analyse how and why.
I know the word "que" is written "quê" when it is the only word in the sentence, like "Quê?", and at the end of a sentence as part of the phrases "o quê", "por quê" and "para quê", but
claims it always becomes "quê" at the end of a sentence. That's an easy rule to remember.
Thanks for your help guys. I am coming to the conclusion that Portuguese is an infinitely complicated language. I lived in Holland for 5 years a long time ago, and I found Dutch much easier than Portuguese is now. The web pages you linked me to suggest that native speakers find this circumflex confusing as well.
Yes, you're right, I should have just said "yes". I'm imposing an English sensibility on the word order which I really shouldn't.
Here Duolingo translates ""Ele está fazendo o quê?" as "What is he doing?" which sounds fine, whereas the literal translation "He is doing what?" expresses a strong element of surprise or is asking for confirmation. There is another sentence discussion with a similar theme: https://www.duolingo.com/comment/666737 where Duolingo translates "Ela bebe o quê?" as "She drinks what?" which made me think word order had more importance than it appears to have.