Frankly, you don't NEED any particular education to call yourself a copywriter or editor. It's not like being a doctor or dentist. Some people fall into it sideways, starting work in the industry in a different capacity and moving a few steps to the left when an opening becomes available. Others study journalism, communications, writing courses etc and get into it that way.
Studying the art of copywriting and editing with a great course under your belt is the best way to get into it, and it can also help you make industry contacts, which can be very helpful to getting an actual job as a copywriter or editor. If you're in Australia, you can study at TAFE or University to get tertiary qualifications, or you can choose one of dozens of independent or study-from-home courses available through different organisations. Just make sure it's reputable and worth the money you pay for it.
Good luck!