Using the dual Youla parametrizations of controller-based coprime factor plant perturbations and plant-based coprime factor controller perturbations, we study the LQG plant-controller continuity question. Indeed, we show that it is possible to calculate a new optimal LQG controller from a previous one when the plant is slightly changed, and to quantify the change in the controller as a function of the change in the plant. In addition, we compute the degradation in the achieved LQG cost when the LQG controller is computed on the basis of a perturbation of the real plant. As a by-product, we characterize the set of all plants that have the same optimal LQG controller.