Welcome to Songwriting Fever. It is really great that you have found this website and I hope you'll find our community useful.
Regarding copyright, I think you do not need to copyright your songs before you submit them since it is very unlikely that someone will "steal" them. Just publishing them here constitutes what some people call "poor man's copyright": http://en.wikipedia.org/wiki/Poor_man's_copyright
Also, note that only members can view your lyrics.However, best practice is to register your work in the US copyright office (http://www.copyright.gov/). This is the only thing that can stand-up in US courts I guess.
Please note that I am not a lawyer and not a US citizen, so the information I gave are generally for information purpose.
Good luck and let me know if you have any more questions.