  We introduce a category of $q$-oscillator representations over the quantum
affine superalgebras of type $D$ and construct a new family of its irreducible
representations. Motivated by the theory of super duality, we show that these
irreducible representations naturally interpolate the irreducible
$q$-oscillator representations of type $X_n^{(1)}$ and the finite-dimensional
irreducible representations of type $Y_n^{(1)}$ for $(X,Y)=(C,D),(D,C)$ under
exact monoidal functors. This can be viewed as a quantum (untwisted) affine
analogue of the correspondence between irreducible oscillator and irreducible
finite-dimensional representations of classical Lie algebras arising from
Howe's reductive dual pairs $(\mathfrak{g},G)$, where
$\mathfrak{g}=\mathfrak{sp}_{2n}, \mathfrak{so}_{2n}$ and $G=O_\ell,
Sp_{2\ell}$.
