Mark01,
If you believe your application has some real value, i.e.; is marketable, it is definitely worth the effort to obtain formal U.S. Copyright(s). As Ingarner points out there is an "intrinsic" copyright afforded the creators of original works under U.S. law, a second method considered to be a form of intrinsic copyright is to submit a copy of the works to the Library of Congress for filing.
It is also vital to establish a "public" record of the timeline, from conception through completion. You should keep a bound notebook with numbered pages (commonly called a laboratory notebook) and carefully record (and date) your progress, kind of like a diary. It is necessary that you have witnesses sign and date your entries frequently; the purpose in this is to develop witnesses to the timeline’s accuracy. A good policy is to utilize a Public Notary as well as several trusted individuals.
All have given good suggestions on this one, mailing certified copies of dated material and other mechanisms are also highly desirable. In short, document, document, document; do it as if it will be used as evidence in a Court of Law.
The reason for all this;
A Copyright can be successfully challenged in Court. Although a formal Copyright tips the scales somewhat to your favor, parties claiming first creation can successfully sue. You may need to prove in civil court (“a preponderance of the evidence,” as opposed to” beyond a reasonable doubt” of criminal coiurt) you were the "first one on the block," and that you did not abandon the endeavor or cease development for any significant period. I’ve seen such battles; typically, the argument becomes “we did it first,” and both sides rush to gather (create) evidence; the best and most evidence tends to prevail.