In this paper, we introduced the concepts of (strongly) $\nu$-conull FDK-spaces, which can be regarded as double-indexed versions of FK-spaces (sequence space with coordinate functionals), by utilizing the notion of $\nu$-convergence for double sequences. We provided fundamental characterizations of these new spaces and established several inclusion relations among them. Furthermore, we investigated the conditions under which the summability domain $E_A^{(\nu )}$ is (strongly) $\nu$-conull, thereby providing new insights into its structural and topological properties.