If you are talking about protecting your logo under the law with a trademark, then it depends. 

Copyright protects original work such as songs, movies, poem, art, architecture, etc, while a trademark protects things that identify a particular business from others like a logo, a brand name, a slogan, a tagline, and more.

As soon as you launch your logo into business, it is automatically protected by the Common Law Trademark Rights, which gives you the rights to use the logo exclusively in your area. A business doesn't need to have its logo protected by the copyright law to launch it in the market. However, with only the Common Law, your logo can still be stolen and used by other businesses, or even worse, they take it and have it protected under their name. That’s why people usually register their logo, slogan, and brand name with the Federal Trademark Registration to enforce and enlarge their right to exclusively use them on a larger scale.

Besides, a trademark lasts for a lifetime and you won’t need to worry about it becoming expired in the future. So it is better for your business to put it under a trademark from the beginning of the operation.