What your ex is doing is none of your concern. She is in your past now. Think more about the future and all those wonderful single girls that you could go out with. That's much more interesting than your ex.
Oh, and about your ex, she probably was psychologically ready to have another relationship by the time she broke up with you, and of course you were not. That's why she was quick but you will need more time to recover. Nothing special, that's fairly typical.