Your model can be upgraded to iOS 6.x.x, but you should not need an iTunes update to do so. Connect it to your computer and open iTunes. Follow instructions below for upgrading from iOS 4.
IPhone, iPod Touch, and iPad iOS Compatibility
Device iOS Verson
iPhone 1 iOS 3.1.3
iPhone 3G iOS 4.2.1
iPhone 3GS iOS 6.1
iPhone 4 iOS 6.1
iPhone 4S iOS 6.1
iPhone 5 iOS 6.1
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iPod Touch 1 iOS 3.1.3
iPod Touch 2 iOS 4.2.1
iPod Touch 3 iOS 5.1.1
iPod Touch 4 iOS 6.1
iPod Touch 5 iOS 6.1
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iPad 1 iOS 5.1.1
iPad 2 iOS 6.1
iPad 3 iOS 6.1
iPad 4 iOS 6.1
iPad Mini iOS 6.1
Upgrading iOS
1. How to update your iPhone, iPad, or iPod Touch
2. iPhone Support
3. iPod Touch Support
4. iPad Support
a. Updating Your iOS to Version 6.0.x from iOS 5
Tap Settings > General > Software Update
If an update is available there will be an active Update button. If you are current,
then you will see a gray screen with a message saying your are up to date.
b. If you are still using iOS 4 — Updating your device to iOS 5 or later.
c. Resolving update problems
1. iOS - Unable to update or restore
2. iOS- Resolving update and restore alert messages