I've been saying since before the invasion that the first thing we should do once the Iraqi army was defeated would be to poll the Iraqis and see if they want to be one, two or three countries. I'm sure the Kurds would opt out.
Then we drag the Iraqi Kurds and the Turks to the negotiating table, but we don't negotiate. We tell them what's what. The Kurds have to forswear all claim to any territory currently in Turkey - if they don't, we won't help them, and they probably never get their own country. In exchange for that, the Turks have to let anyone in Turkey emigrate to Kurdistan freely and without penalty. We point out that this will let them get rid of a lot of dissidents, and they will score loads of brownie points with us. If either side invades the other, the US will come in militarily on the side of the invadee. Simple. Everybody wins.
And with most of the oil in Iraq now in the hands of the Kurds, if the rest of Iraq winds up being hostile to us, at least they won't have a lot of oil money for a resource.
