Ginny is a fun nickname, a slight variation from the ever-present "Jenny" of my generation. (Of course, because Jenny is now a "mom name" it would itself be quite unique on a little girl). Anyways, Ginny is also featured in Harry Potter. There are some pretty unique options if you want to use Ginny for your little girl!
Virginia - I think that Ginny is most often derived from Virginia. Virginia is of Latin origin, it originally referred to a certain tribe, and means virgin or maiden. It is of course strongly associated now with the U.S. State, but maintains status as a name as well in popular media such as the famous letter "Yer Virginia, there is a Santa Claus"
Ginevra - This is the Harry Potter name that they use to derive Ginny. It is of Italian origins and means fair and smooth. It is actually considered a variation of Jennifer.
Imogen - I have heard a lot of buzz about this name recently. I ran into it when reading the novel Middlesex, and had to look up the pronunciation, which it turns out is actually kind of controversial. The "I" is soft, but other than that there are some variations. I see both i-moe-jen, i-moe-jean, and the softer more flowing im-a-jin, where the middle syllable almost disappears and is just a swivel point for the rest. Anyways, Imogen is Celtic and means maiden. It also is found in Shakespeare.
Genevieve - This master of nicknames was already discussed once when I was looking for a source for Evie. It means white wave and is strongly associated with Saint Genevieve.
Eugenia - The much less used feminine version of Eugene (which in and of itself is not too popular at the moment). Eugenia is Greek and means well-born, or noble. Concerned that it should lead to the nickname Genny rather then Ginny? You can use the variant spelling Eugina (note the slightly different ending as well).
Regina - This name is of Latin origin and means Queen. It was a nickname for Queen Victoria.
I am sure I am missing other options. There are a lot of names that begin with "gin" that I suppose could also get you to the nickname, but I don't feel like featuring these names because they are either so short as to not need a nickname (Gina, Ginger), or I prefer a different spelling (Jeanette, Janelle).
Do you like the nickname Ginny? What name would you use to get there?