I think the sentence refers back to what was said just a little earlier. Phyllis said "Don't be foolish. Sit down. Isn't washing one's head awful?"
So I think when she says "You are--aren't you?" she means to say "You are foolish, aren't you?". She's making fun of his feeble answer. I think it makes sense because she was also making fun of him earlier when he was looking in the mirror and it says "A clear, high, mocking voice said 'Oh-h! Conceited young man!'"