grammaticality - Asking a question with "have" without do-support: "What symptoms has Anne?"

The context is that a doctor is asking about somebody's child's symptoms of influenza.

Is this question correct: "What symptoms has Anne?" If it's incorrect, then why?

It looks strange to me, I would rather ask "What symptoms does Anne have?" but don't know why.

Answer

As John Lawler says in a comment, this use is possible in British English. But even in Britain, it is rather old-fashioned or literary. The normal British form would be

What symptoms has Anne got?