In fairness, I just looked at when the book was published and it was wen I was 16/17 and not 13 (time seriously flies, it's crazy! It feels like ages ago!). It's hard because on one hand, 13 might be too young to process that material, but on the other I think the topics are things teens are having to deal with at younger and younger ages.
I don't blame you for not wanting to watch that or her wanting to watch it with you - I know I probably wouldn't have when I was 13. I would just maybe make it clear that you are always willing to have an open dialogue about it if she wants.
Man...Terrified of having kids some day because these seem like difficult parenting choices to make!