We propose a quasi-three-dimensional frequency-domain model to investigate the lasing modes of an InGaAsP/InP quantum-dot microdisk laser. The model requires a complex susceptibility to solve the electromagnetic fields of the microdisk laser. We use the model to investigate the size limitations of the quantum-dot laser by evaluating its performance through the cavity quality-factor (Q-factor), from which the linewidth can be inferred. We find that higher order modes with high Q-factors ( 2.4 × 104) and consequently narrow linewidths ( 65 pm) propagating in the 1.5 µm wavelength region can be sustained in a microdisk laser with a radius as small as 1.6 µm and a thickness of 200 nm. Our model can be used to study other types of microdisks provided that the susceptibility of the medium is known.