That book should have a bloody content warning on it. It's seriously grim and yes I know it's satire and I don't think it should be banned - but it's fucking awful and gigantically misogynistic, satire and all.
I think you've handled this really well though - discussing it honestly with her and suggesting alternatives is about the best you can do with 13, and she may well listen to you especially as she seemed to have misunderstood the contents.
God knows I read some unsuitable shite at that age but I didn't seek out books that were known for being actively disturbing, I'd already stumbled on enough of them by accident to know I wouldn't enjoy it.
Some of the adultier books I read around that age that really stayed with me that are on the theme of 'The Human Condition': Brideshead Revisited, Jane Eyre, A Tale of Two Cities, Catch-22, DH Lawrence. I also read a load of scifi and Martin Amis that was on my parents' shelves but I wouldn't recommend it!
And some really good grown up reads that I think 13 is ok for but are definitely more adult themes with some shagging and violence: Outlander, any Hilary Mantel, The Girl with All the Gifts (gory mind you), Audrey Niffenegger, Ian Rankin (either the straight novels or the scifi).
I don't believe in preventing young teenagers from reading adult books, they are in the process of becoming adults, but I think you've done well to steer her clear of this one.