Kakashi is DEAD if he even looks at her!
Buuut Seems like a good, even matchup. Kakashi knows the water dragon jutsu and if he copied that one jutsu of Zabuza's then he also knows that whirlpool jutsu, not saying that those are his only water jutsu. If he gets Konan wet then that would seriously hamper her movement, but that is a major weakness to her paper jutsu so Konan may know of a way to counter it or she'll just have to avoid it.
Konan on the other hand can manoeuvre around a battle field quite easily, when she goes into that Angel mode, and her ability to freely control the movements of her paper can be quite devestating. An example would be manipulating paper bombs and moving the opponent around a battlefield according to the way she wants.
Of course in the end I think Kakashi would win, due to the lack of battle info I have on Konan anyway