We study the spontaneous emission (SE) dynamics of a QE near a graphene nanodisk. We analyze the excited state population dynamics, quantify its features using different non-Markovianity measures, compute the quantum speed limit of the dynamics, which can be achieved under the given coupling conditions. More specifically, we investigate the SE dynamics of the excited state population of a QE modelled as a two-level system located at 5 nm and 15 nm from a graphene nanodisk of radius 30 nm, while the free-space decay time of the emitter lies between hundred picoseconds and microseconds. At close distance and for short free-space decay times of the QE, the observed dynamics shows strong non-Markovian features; as the distance from the nanodisk or the free-space decay time increases, the non-Markovian features in the dynamics diminish. These findings reflect the transition from strong light-matter coupling to weak coupling conditions. Under strong coupling conditions, we also observe pronounced decaying Rabi oscillations and population trapping effects in the excited state population dynamics of the QE. We also quantify the non-Markovianity of the SE dynamics by computing different measures and the quantum speed limit for each case, obtaining large measures values and potentially large quantum speed-up for the dynamics under such coupling conditions, while both properties are decreasing as the coupling weakens. These results and the observations related to the QE excited state population dynamics under strong coupling conditions are in agreement. Evidently, the graphene nanodisk can become a platform for achieving strong coupling conditions for light-matter interaction at the nanoscale even for large free-space decay times and at large distances between the quantum emitter and the nanophotonic structure in comparison to metallic nanoparticles.