My best friend wants me to marry her and her boyfriend in October of next year. We live in Virginia. She found an overlook in the mountains, but it is just across the North Carolina line in Alleghany County.

My question is: I have the original Ordination Certificate that was sent to me from ULC. Will this be enough to marry them outside my home state? What else might be required?

The laws in Virginia and North Carolina are slightly different regarding marriages. You need to call the county clerk or marriage license office in the county where they plan to file the license. It looks like it is cheaper to get a marriage license in Virginia, but I think you have to register to officiate the ceremony.
My wife and I got married in Alabama, and we filed the license, and so were legally married well before our actual wedding ceremony, which was performed by our friend also. This removed the stress of worrying about the legality of our actual wedding!