Surely "what type have you" is also a correct answer!
That's not acceptable in my dialect, but I do believe it's common in Hiberno-English and some dialects in the UK, so it should possibly be accepted.
Still not accepted
Should definitely be accepted
What kind have you? Also needs to be acceptable!
Out of curiosiy, how would you ask "What type are you?"
Cén cineál atá tú?