No, we do not. Your song's copyright is protected at the moment of creation and fixed in a tangible form that is perceptible with the aid of a machine. This is true for both published and unpublished works.
Songtradr does recommend filing for copyright registration of your works with the copyright office. You will need to register your copyright in order to bring a lawsuit for copyright infringement in the United States.
The process to register copyrights is different for each country. Please contact the copyright office in the country where the work was created for more information.