Keep in mind that if you do get accepted to Princeton, it's incredibly easy to change your major / department (i.e. into or out of engineering) once you get here. I'm not sure how much being female matters here since our gender ratios in engineering in general are pretty balanced (I think?) while bio is, at least nationally, becoming more female-skewed. (In contrast with, say, physics / math / computer science.)
It sucks that nobody really knows what "engineering" means until you get to college! I mean, people are like, "oh, well you're good at math / physics / science, you could be an engineer!" but nobody really tells you what that's like. As an "engineer" who picked CS pretty early on, I /still/ don't know, since the freshmen eng curriculum for most people is just basic science and math.
One thing to consider if you come here is the Integrated Introduction Engineering, Math, and Physics course for freshmen: Princeton's Keller Center: An Integrated Introduction to Engineering, Mathematics, Physics (EMP)
I've heard it's lots of work but very good -- you build rockets in your labs instead of doing normal (terrible) physics labs, etc.
If you're debating between maybe chemical engineering or molecular bio, I would say that if you were to go to Princeton, talking with current ChemE majors / bio majors / etc and taking bio and chem classes would be the way to go. As long as you take care of your freshmen engineering requirements + take some bio, you would probably be able to decide by the end of freshman year. Talking to upperclassmen is a biggie.
As for applying? I don't know. That's a tough one...I'd honestly say that you're good either way. If you apply to be ChemE, then your science EC's will still look good and obviously relevant, so it probably doesn't matter too much for you.