Good point. Googling "Dost thou havest a " turns up two results, one of which is Eliezer's comment.

On the other hand, my instincts aren't perfect. I'd have bet that "havest" wasn't a word, but it is. "Hast" is a contraction of "havest".

I was wondering whether the problem was that "dost havest" is redundant, but "havest thou a" doesn't turn up anything period.