Is the set of minimal DFA decidable?
Given two DFAs $A,B$, it is decidable (even efficient!) whether $L(A) = L(B)$: use the product construction to get a DFA for $L(A) \triangle L(B)$, and now use reachability analysis.

In order to determine whether $A$ is a minimal DFA, one can just try all DFAs $B$ with less states, looking for one satisfying $L(A) = L(B)$. Alternatively, there are algorithms for minimizing DFAs which are vastly more efficient than that approach. They are even more efficient if all you want to know is whether the DFA is minimal or not.