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Hi,I'm Zoey.I'm reviewing your post. Please be patient as I may need to research for you, and it also takes time to compose and type a reply.
Yes, you'd be breaking the law. You could be prosecuted Federally under the Mann Act for transporting a minor across state lines for immoral purposes. Not a good idea.
It's not the distance that matters. It's the fact that the Federal age of consent is 18. So if you're planning on either transporting her or making arrangements to meet her for sex in another state, you're risking a Federal offense.
Because you're missing the point that Federal law is different from state. Under her state law, she's not capable of consenting to sex and under Federal law, she is not legally capable of consenting to travel for sex.
You asked whether you'd be breaking any law. The reality is that yes, you would be breaking Federal law if you're caught.