I actually know two girls named Virginia! One is 20 and goes by Virginia, and the other is 18 and goes by Ginny. The twenty-year-old has siblings Hope and Peter, and the eighteen-year-old has a brother, Charles (called Charlie).
I'm going to have to disagree with the masses on this poll and tell you I absolutely hate the nickname Ginger - it seems incredibly dated to me. However, I do think that Ginny (especially since the Harry Potter series) is a fresh, cute nickname option.
Here are some sibling names I'd suggest for Virginia:
Many of these would make beautiful middle names, too!
Do any of these fit what you were looking for? My favorites are Virginia, Caroline, and Adrian, personally.