Spin-polarized vertical-cavity surface-emitting lasers (spin-VCSELs) with birefringence-induced polarization oscillations have been proposed to generate desired photonic microwave signals. Here, we numerically investigate the generation of photonic microwave signals in an optically pumped quantum dot (QD) spin-VCSEL. First, the influence of intrinsic key parameters on period-one (P1) oscillations and microwave properties is discussed. Second, the difference between microwave generation based on the quantum well (QW) and QD spin-VCSELs is analyzed by controlling the carrier capture rate that is described in the spin-flip model. The QD spin-VCSEL shows superior microwave quality in the low-frequency range (e.g., 10 GHz~20 GHz) compared with the QW spin-VCSEL. Finally, to boost the performance of the generated photonic microwave signal, optical feedback is introduced. The results show that dual-loop feedback can simultaneously narrow the microwave linewidth and suppress the side modes that are derived from the external cavity mode.