This paper reports on the emission characteristics of amino-functionalized graphene quantum dots (af-GQDs). We employed the variable stripe length method to measure the net optical gain of af-GQDs. Photoluminescence emission was enhanced through the efficient confinement of photons using an optical resonator. The two-dimensional resonator is made up of a cholesteric liquid crystal (CLC) reflector to enable the redistribution of spontaneous emission from the af-GQDs. The proposed method was shown to increase the intensity of peak emission to more than three times that of the reference sample without a CLC reflector. The peak emission intensity of af-GQDs in the optical resonator grows exponentially with an increase in excitation energy. These results demonstrate the feasibility of two-dimensional optical amplifiers based on CLC reflectors.