You don't need to work for, or with, any major haulage firm to find work as a courier. All you actually need is a car. If you want to make major money from it, though, you'll also need a keen mind for planning. The key to making money as a private courier is to string several jobs together on the same route.
Usually, you'll want to make one major trip a day, so find an item to transport from place A to place B, and agree a price for it. Then hunt down other jobs that are in or around the same route, and factor them in as stops on the way. The average charge for transporting something, although it varies, is around $40. Fit in ten deliveries a day and you're well on your way to a very comfortable lifestyle. Soon you'll be able to hire a second car and driver to help you out. One day you'll need a whole fleet!