I don't think of it as dated (I'm in the UK) because although it was common, it's not tied to a specific year or era in the same way other names are.
Georgia has been used for a long time.
I dislike
Georgie. All the
Georgia's I know go by their full name or
George.
Georgie is saccharine.
My favourite feminine form of
George is
Georgia, followed by
Georgina.