Currently, much interest is attracted to investigating the potential of hybrid systems that exhibit plasmon-induced photoluminescence (PL) enhancement of quantum emitters in terms of optoelectronics and biosensing applications. The implementation of these systems based on photonic microcavities offers benefits due to a stronger localization of the field within the resonant cavity. Porous silicon is one of interesting materials for engineering such microcavities thanks to the simplicity of its fabrication and the possibility to embed emitters from the solution into a ready-made resonator. In this theoretical study, the fluorescence enhancement of a quantum dot (QD) in a hybrid system based on a porous silicon microcavity (pSiMC) and silver nanoplatelets (AgNPs) was investigated using finite element method (FEM) numerical simulations. For this purpose, infinite arrays were simulated by using a periodic unit cell. The pSiMC was designed as two λ/4 distributed Bragg reflectors with alternating refractive indices and a cavity layer of a double thickness between them. For comparison, simulations were also performed for an AgNP and a QD in a reference monolayer with a constant refractive index without a microcavity structure. The results show QD fluorescence enhancement in the AgNP/pSiMC hybrid system, mainly due to the higher excitation rate.