I don't find
Fawn ditzy; I'd say it's more sweet/nature-y than outright cute. I would prefer to see it as a middle or nickname, but I wouldn't balk at it as a first. Feel-wise I mentally associate it with
Farrah for some reason.
I happen to quite like Faline as a name; with the association of
Bambi's girlfriend, I could see
Fawn possibly being a nn for that. Sound-wise, it could work as a nickname for
Ffion or, as a bigger stretch,
Fallon.