While, you don’t technically need to copyright your work as an indie publisher, it’s a good idea. It’s not expensive and can be done online.
Sadly, the eCO site where you register your work is in desperate need of a UX designer. Seriously, it’s so unfriendly as to be a stereotype of government obfuscation.
My advice to anyone wanting to use eCO to register your work is to get comfortable and be prepared to read through a lot information and click on many links you don’t actually need. Here’s a tip, scroll to the bottom of the page for most of the links you do need. Essentially, expect not to find what you need anywhere you would normally find it on another website.
Once you understand that, the process goes along smoothly.