Since 1978, the copyright laws have changed in the creator’s favor. Now, anything you create automatically is copyrighted to you. This means that, legally, this piece of work is yours and will be recognized as such. Now, that doesn’t mean you can just ignore registration and be totally fine. To obtain the full protection the copyrights provided, you have to legally register the copyright in your name.
For example, the statutory damages rule states that the court can fine people for infringing on your copyright. Without registering officially for said copyright, the court will not fine people. While, yes, your work has minimal coverage upon completion, registration with the copyright office is the only true and definitive way to gain access to all the protections the law offers.