I like
Georgie, but I think that it's important to consider how she will want to introduce herself so I would name her
Georgia. I dislike
Georgina because it sounds a bit old fashioned, which is also why I prefer
Georgia.
If
Georgia is too mainstream, (even though IMO I think the NN
Georgie makes it more original) here are some variants apart from
Georgina:
Georgeann
GeorgeannaGeorgeannah
Georgeanne
Georgena
Georget
Georgett
Georgetta
GeorgetteGeorgianaGeorgianah
Georgiann
Georgianna
Georgiannah
Georgianne
GeorgineGeorgya
GiorgiGiorgiaJorja