I am not certain precisely what you are asking, but any linearized action of $\textbf{PGL}_{m,k}$ on a variety $Q$ that has one dense open orbit will have geometric quotient $Q//\textbf{PGL}_{m,k}$ equal to a single point, which is smooth. Of course $Q$ need not be smooth, e.g., the action of $\textbf{PGL}_{3,k}$ on the parameter space $Q\subset \mathbb{P}H^0(\mathbb{P}^2,\mathcal{O}(3))$ of nodal plane cubics (which is highly singular).