It's natural and correct.

Since the person being referred to is dead. She can no longer be 22 next week (get any older). Also, since she is dead, she would have been (in the sense that it cannot be acheived anymore now). You have to use "would have" to show something could have happened, but for some reason cannot anymore. Other examples are: I would have hit her right then, I would have called her tomorrow. I would have taken the class next semester. The topic has been referred to in some way previously in the conversation.