Qualifications
If you want to own the company, you generally need to get a license to operate within your state (source). If you want to work on a catering staff, you need to be able to carry things and have the ability to follow basic commands. Believe it or not, not everyone you'll meet in catering will be able to do those things.
Some regions don't allow catering out of a home kitchen, so it's best to check with your local Board of Health before setting up one in the shack in your backyard.
As far as what will probably help you in the long run, it can't hurt to know how to cook, market, and run a business. Besides culinary school (a no-brainer for you aspiring chef-owners out there), there's a lot that you can learn from taking a couple of food management classes. They'll help you organize finances and price services in a way that the financial app on your smartphone just never could.
Caterers can also join the National Association of Catering and Events. This association offers executive caterer certification, business classes, and event coordinating workshops. You'll be able to put your client's mind at ease when you show them your credentials.
We're just kidding—they're not going to care anywhere near as much as you do. Just make good food and get it to them when they want it, and you'll do just fine.