It's retro chic and cute, but not one I'd use myself simply because it's not really my style. It would be refreshing for a child these days, though.
Elizabeth is a beautiful name. I like how it lends itself to a variety of nicknames.
Elizabeth is very common, but at least she could go by a relatively uncommon nickname. I'd rather meet an
Elizabeth "
Betty" than an
Elizabeth "
Liz."