Oh, sorry, should have noticed that.
No, the iPad3 cannot be jail broken on iOS 5.1. The only jail break for that iPad right now is on iOS 5.1.1, but you can't move up to that version as Apple has closed the authorization window for it. The only iOS you can upgrade that iPad3 to is iOS 6.0.1 (the one currently authorized by Apple).
As I highly doubt a jail break will ever appear for iOS 5.1, I'm afraid my only advice to you is to go ahead and upgrade to iOS 6.0.1 and join the rest of us who are watching this thread for a jail break for that iOS.
Marilyn