I like Frederica. It's not a name I'd give my daughter if I had her, but I don't consider it ugly or too old-fashioned. You can get very cute nicknames, like Erica, which is a name that I love and, well, there is nothing wrong with this name. Frederica... Why not?
This reminds me of a silly girl with a lot of freckles and her front tooth missing! I think it's unique and Erica is a great nickname! Wacky and happy! :)