Alan's suggestion is a good one. When it comes down to it, it's all about what you can prove.
You don't need to apply for or submit your music somewhere to be protected by copyright, but the music must be "reduced to material form" (which basically means that ideas aren't protected). The
moment that you reduce it to material form the copyright will vest in the author, and it is this date that you need to be able to prove in a copyright infringement case.
Long story short: When you hand someone the music to play on a CD, the music is already copyrighted.
Short story long:
A recording isn't the only way to protect your music though.
This is what is classified as a musical work in the copyright act:
“musical work” means a work consisting of music, exclusive of any words or action intended to be
sung, spoken or performed with the music;
You'll notice that the term "work" is used, to keep it "format neutral", if I can call it that.
Now look at the requirements of a "work":
A work ... shall not be eligible for copyright unless the work has been written down, recorded, represented in digital data or signals or otherwise reduced to a material form.
So a work can be written down, recorded, represented electronically or otherwise reduced to material form. Ideally you'll want as many formats as possible covered, which gives you a lot of stuff to prove your copyright claims with. A recording will be cool, a recording and sheet music would be cooler. You can have the hard copies of the sheet music date stamped in front of a commissioner of oaths for example (conveniently located at you local cop shop) and keep the originals filed away safely.
Hope this help!
R.