We consider a gauge-singlet vector-like fermion dark matter model that also contains a gauge-singlet scalar and an SU(2) singlet vector-like quark. The dark matter has a tree-level coupling with the gauge-singlet scalar but communicates with the standard model via loop-level scalar-gluon-gluon and scalar-photon-photon effective couplings induced by the vector-like quark. The main focus of the paper is to study the implications of such effective couplings. We also include the Higgs-portal coupling of the dark matter due to scalar-Higgs mixing. In the model parameter space, we present the dark matter relic-density, the dark-matter-nucleon direct-detection scattering cross-section, the large hadron Collider diphoton resonance signal rate, and the theoretical upper-bounds on the fermion-scalar couplings from perturbative unitarity.