The theory $\mathrm{ACA}_0$ is not reflexive (because it is finitely axiomatisable and cannot prove its own consistency). So how, if at all, is it possible to prove that $\mathrm{Q+Con(PA)}$ cannot be interpreted in $\mathrm{ACA}_0$?

(I am assuming that for an interpretation of the second-order language of arithmetic, the domain of the number variables must be interpreted to be a set of numbers which is definable without parameters.)