Cockayne's monotonicity conjecture for domination numbers of Queens' graphs

Let $\mathcal{Q}(n)$ be the $n$-Queens' graph, and let $\gamma(\mathcal{Q}(n))$ denote its domination number. Cockayne's conjecture. For every $n \in \mathbb{N}$,

$$\gamma(\mathcal{Q}(n))\leq\gamma(\mathcal{Q}(n+1)).$$

This asks whether the domination number is nondecreasing with the order of the Queens' graph. The source presents it as an open problem proposed by Cockayne; no resolution is supplied.