Yes, that is what you need to do. The employees at the AT&T store may charge you anywhere from free to $25 for the new SIM, so use that information as a frame of reference. It has been stated that if you add money to your account while you are still inside the store, they will waive the cost of the new SIM card.
You will be able to keep your current prepaid plan and you can still choose to add money to your account by refill cards like you currently do. I do it the same way.