iOS 6.0.1 was just released a few minutes ago, but we've already confirmed it can be jailbroken right now using the existing jailbreak tools for iOS 6.
Although RedSn0w was recently updated to 0.9.15b3, the update doesn't yet include support for iOS 6. That's okay, because you can still point at the already supported iOS 6 firmware and successfully jailbreak iOS 6.0.1.
Check inside for the full video walkthrough that shows how.