You are correct it is “For what”, but to mere mortals, just keep it simple.

Also, it’s a sentence that assumes a silent context. The full sentence might be “That is for what?”, which has components of a complete sentence – subject (That), verb (is), complete prepositional phrase (for what). The prepositional phrase isn’t necessary, but at least it works that way.

Response to Karol:

You’re probably right. I had a really good teacher, though. I didn’t understand this stuff in high school, but the course instructor made it seem like a snap. The preposition was one of the first things we learned about. Thanks for the input; I didn’t mean to over do it.

as in

for what do I owe the honor of your presence…..

as opposed to

what for do I owe the honor of your presence…..