Qualifications
There are technically no qualifications for this job other than the talent you'll need to come up with your designs. We'd gently suggest that you go to a trade school or training program, but it's not required. In six months or a year of a program, though, you could learn how to identify and grade precious gemstones apart from your own lame birthstone. You'd also learn how to actually design jewelry and use those scary tools to polish, cast, and set all the shiny, expensive things.
Another inroad to the jewelry designing life is an apprenticeship, but that's hardly a viable option these days. It's precisely the rise in DIY designing and Internet self-promotion that has caused a drop-off in the more traditional methods of jewelry creation. So just do it like everyone else: dream up designs in your head, figure out how to make your ideas come to life, and get yourself to every trade show within a hundred miles to sell your products.