I'm with HaroldU, Mrs. Jones, and Joni's copyeditors on voting for the question mark. In addition to the other points made, it would eliminate the potential of pulling readers slightly out of the story by having them wonder, "Wait, if she just asked a question, why isn't there a question mark?" I think our brains are just trained to expect a sentence that starts with "Why" to end with a question mark, unless it's an exclamation.
Fwiw...