I agree, she needs to take a pregnancy test. BEign as she is young, it's not uncommon for her cycles to be off once in awhile, but since you are having unprotected sex there is a chance of pregnancy. Take a test and see what it says.
You guys should do a home pregnancy test right away. If she's six days late and she's pregnant, the test will be positive for sure. Then you can discuss what you guys want to do. Re: when women are fertile, you'd be surprised what an inaccurate science that really is! Glad you've learned your lesson about always using protection. Perhaps she could go on birth control? Any way, I wish you guys the best and hope everything works out for you.