Well, Ben seems to be 40ish. Jack said so, and it fits with the car models we saw when Ben was born. Annie seemed to be about the same age. The actress who plays Charlotte is about 25. So, do you reckon early 20's is the youngest the character could be? If so, yeah it's possible she could be Annie's daughter.
I would bet money (well, a small amount) that she lost some loved one in the purge, so could be Annie.
In answer to another question, it doesn't appear that Annie died in the purge. If she had I think we would have seen Ben take a moment over her body, so as far as we know she's alive somewhere.