Exceptional points have been studied in a plethora of classical optical systems and can dramatically modify the optical response of the studied system. Recently, there is increasing interest in applying the exceptional points formalism in fully quantum systems to achieve efficient control at the quantum level and show the drastic effect exceptional points have on the system's properties. In this work, we theoretically study the effect of quantum exceptional points on the optical properties of a quantum dot placed inside an optical microcavity and interacting with a weak probe field. For the analysis of the system, we use a quantum approach, where we model the quantum dot as a two-level system and describe the light-matter interaction with the proper master equation, including the spontaneous decay and the pure dephasing of the quantum dot, as well as the decay of the optical cavity. We also define the effective non-Hermitian Hamiltonian of the system and derive the necessary conditions for the formation of an exceptional point, the point where the eigenvalues of the Hamiltonian coalesce. We then study the steady state behavior of the system and calculate the optical susceptibility from the coherences between the vacuum and the system. By separating the total susceptibility to two equivalent susceptibilities, corresponding to fictitious free quantum emitters, we show exceptional points drastic effect to the optical properties of the system close to the region where the exceptional point is formed. We further examine the optical properties of the system in the regions of the parameter space that arise from the exceptional condition, namely the strong (coherent) coupling regime and the weak (incoherent) coupling regime.