iOS 6.0.1 now available, iPhone 5 users need to download installer

iOS 6.0.1 was just pushed to iPhones and iPads running 6.0. The update is 34.7 MB and contains various improvements and bug fixes, including:

• Fixes a bug that prevents the iPhone 5 from installing software via over-the-air updates.
• Fixes a bug where horizontal lines might be displayed across the keyboard
• Fixes an issue that could cause the camera flash not to fire
• Improves reliability of the iPhone 5 and fifth-generation iPod touch when connected to encrypted WPA2 Wi-Fi networks
• Resolves an issue that prevents the iPhone from using the cellular network in some cases
• Consolidated the Use Cellular Data switch for iTunes Match
• Fixes a Passcode Lock bug which sometimes allowed access to Passbook pass details from the lock screen
• Fixes a bug affecting Exchange meetings
• The update is available via Software Update on your iPhone or iPad or the next time you connect your iOS device with iTunes.
• Note that iPhone 5 users will have to download an updater app first, which will then prompt them to update iOS. The FIRST updater will appear in General > Software Updates as normal updates would appear. It will then prompt you to launch it, send you back to Software Updates and the update to 6.0.1 can continue. There is no need to search the store for this app.

Update: It seems Verizon iPhone 5 users will need to reboot after the iOS Updater app is installed, whereas we can confirm AT&T iPhone 5 users do not.

Update 2: Apparently some AT&T users might have to reboot for phase one (the iOS Updater app). Your mileage may vary, apparently. Further, Sprint customers will also reboot.