Hmmm. Jodie/Jody is all right. I prefer Jodie. I know three, two spelt Jodie and one Jody. I've also seen Jodhi, but my mind just screams NO! It makes me think jod-hee in pronounciation.
I don't think Jodie's too nicknamey. I've never known it as a nickname, just a full name. It does seem popular on people born in the 70s, and to me it is a bit 70s dated, but still usable.