In this paper, we study a second-order $q$-Cesàro matrix and its matrix domains in the spaces $c_0$ and $c$. We establish basic structural results, including inclusion relations, connections with earlier Cesàro-type sequence spaces, the duals of these spaces, and the associated matrix transformations. Our approach extends known work on $q$-Cesàro operators and provides a starting point for further investigations of higher-order $q$-averaging methods in summability theory.