Most likely, no you do not. It is not a requirement. If you go this route, ensure the brakes are still in good working order (pad thickness and rotor warpage/thickness). Also ensure you do not leave any grease or other kinds of oils on the rotor during replacement, as this will contaminate the brake pads and they will not perform as expected afterward.
As an aside, if you have ceramic brake pads, I've seen these smoke quite often when they first cure. It surprised me the first time it happened to me, but after that found it to be quite common. I'm going to assume since you've already had them on there for a month, they've had several good heating cycles. If not, it may be something to consider.