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It sounds like some malware. Malware apps like to root phones in order to secretly download apps and keylog your phone. I would do a factory reset on your phone. The sooner, the better!
Please read http://androidforums.com/android-applications/36936-guide-how-find-safer-trusted-apps.html for information on how to protect yourself from malware.
I haven't heard of a successful attack on a Gingerbread-equipped device, but it certainly does sound like a malware attack.
Also, install the following: https://market.android.com/details?id=com.joeykrim.rootcheck
That'll help you establish if your phone really was rooted. Maybe AVG is wrong.
I've never heard of malware rooting a phone without the user's knowledge. Source?