Either way, just be careful. As the father of an awesome little girl myself, I can easily relate to strict parents! lol
Keep it simple. At your ages, 2 years seem like forever. When you get to be my age, you'll freak out with every b-day because you're too aware of how fast your time is running out.
With that in mind, keep your priorities straight. In HS and college, your main purpose is completing your education, not expanding your social life. After that, you're trying to get a solid footing in your career. And even that is never a guarantee, but a few short years of experience go a long way towards making you less shaky in the worst of times if things ever do get ugly. You're in good shape by your mid-20's, and you'll have a good social circle that makes dating a breeze.
If you really love this girl and she really loves you, the time will go fast. For MOST young people, waiting that long seems to take fooooooorrrreeeevvvvvvvverrrrrrrrrrrrr. I have NEVER been in a LDR for any length of time that I didn't cheat on my gf. I'm just not cut out for it. As I got older, I learned not to expect fidelity from my partner, either.
The advantage of waiting for a girl with strict parents is even though you can't date her, neither can anyone else. You'll likely want to see other girls. It would be a bad idea and in poor taste to mention seeing someone in the meantime, so keep that to yourself. Likewise, it's best not to ask if she has a bf. Keep in as regular contact as you can without putting any pressure on her. If it's meant to be, you'll get to see her once she "ages out."
Also keep in mind that at your age, a LOT can happen in a short time. I recall falling hard for a younger girl even though I was IAR in HS. We'd write letters from time to time, see each other for a week over the summer, and lost contact once I left for college. I knew her as this short, flat-chested, knobby-kneed little thing with a very sweet demeanor and personality. Then she just shows up one day and she's tall and, um, VERY feminine. All grown up. NOT the girl I thought I knew. I had a little more freedom then, we tried a serious relationship, and by the time I finally gave up on her, I had to admit she was fickle and not really a very nice person. She wrecked my whole outlook on women--but that outlook needed an extreme makeover anyway. She was my wrecking ball and I was her blank space. We're good friends now. Back then she was a golddigger. So it took YEARS before we got back on speaking terms.
The takeaway here is time does things to people. I hope this doesn't happen to you. Just be prepared that the next time you get to see her you won't recognize her. Be supportive. Be forgiving. Be understanding. Time does NOT take away who you are. You will always be who you are, she will always be who she is. My ex now is the same person as that little girl I loved, and my feelings haven't changed (same is true for the other girls I dated). It's a question of whether it survives the test of time. Don't take that up as a challenge. Don't force it to work. Don't try to be the hero. Don't, PLEASE, don't play Romeo to her Juliet. Don't fight it. If it means that much to you, give it an honest try when the time is right. Don't feel like you're obligated to wait for her. Live your life until she ages out, THEN make a decision about seeing her. Stay in contact any way you can for as long as it works out. Don't give each other too much info on your personal lives, don't put your life on hold.
Good luck, and best wishes with everything this fall! Having been there/done that and now in the business of prepping kids for life after HS, I can say it's gonna be quite a ride. Hang in there!