Well, I'm not going to preach too much to you about the age difference even though I'm totally against it and think you're nuts.
For God's sake, whatever you do, don't have sex with her till she's 18 no matter what, provided things work out and you're still together. I don't know what the age of consent is here but I sure wouldn't chance it. Don't want to see you back here about statutory rape, child support, custody and visitation.
I don't know about her moving out. I don't believe it's possible though unless her parents grant her permission and go through the proper legal channels.
You may want to call the magistrate and just ask them if it's possible for a 16 year old to move out to a relatives and how they would do that legally, ect.
Also I'm giving you the link to the NC General Assembly. It has a search engine where you can put in key words and it will pull up different statutes.
[url]http://www.ncga.state.us[/url]