If the door is affected, the rocker will be also.
I suggest that you buy something to stop the rust now, not a fix or a solution, but the first step. Skip the quick fix rust magic stuff you see at parts stores. Those cannot touch rust in seams, which is where all of your rust began.
Go to Eastwood, find the Rust Dissolver, and buy a quart or a gallon. That is the best product to stop rust in seams, it flows exactly like water. You put it in a spray bottle, and spray it on, into any rusted seam you can find.
It isn't magic, rust removal is the hardest thing to do. Ideally as much of the rust should be ground or sanded away as possible. But in seams that cannot be done, so a thin viscosity product is the only chance to stop rust.
I used that product from Eastwood, when it was called Oxysolv, as my first step on rust. It can be painted over directly(wipe it dry like a final prep). I followed it with Rust Encapsulator, which is better than POR 15.