Uh. Princeton doesn’t allow people to apply in junior year, as far as I know. It’s stated in their website FAQs.
I would go ahead and apply. I know of a guy in my area who is at MIT after sophomore year and a girl who is at UVA after finishing junior year. Even though to be fair, the sophomore is one of those genius kids who makes it on the news, its not out of the realm of possibility. Even if you don’t get in this year, you can always try again the next. Just email the admissions people to see what they say. I think you have a decent chance, although your ECs could use a slight buff.
Thanks for pointing that out @icarus29, I was looking for their policies but didn’t find that.
I had much the same academic profile as you through junior year including being VERY far advanced in math. However, I wouldn’t have even considered leaving after junior year and applying to colleges. I was very involved in school in sports and clubs where I held leadership positions but I also spent most of my four years heavily involved in outside research which I could not have completed before senior year. I’m certain I was a far better and more prepared applicant when I did apply senior year. I was accepted either early or with likely letters to the HYPSM schools that I applied to (I only applied to three schools). Unless you have accomplished something truly extraordinary, most schools do not view your being a year younger than everybody else as any kind of benefit. To the contrary, they have to worry about your maturity level and the fact that you will be a minor longer than other kids which might prevent you from working in certain labs, etc. Also, when your classmates reach drinking age you will not and this is a potential liability for them if you attempt to join in with them in public spaces. Good luck with whatever you decide but if it were me I would stay put and work on developing more of your talents that would allow you to not just stand out in colleges applications but also to thrive once you arrive on campus wherever it may be.