But don't take my word for it, listen to the federal government:
"Copyright protection subsists from the time the work is created in fixed form. The copyright in the work of authorship immediately becomes the property of the author who created the work. ... The way in which copyright protection is secured is frequently misunderstood. No publication or registration or other action in the Copyright Office is required to secure copyright. See the following note. There are, however, certain definite advantages to registration. See Copyright Registration on page 7"