The transmission of a two-level quantum emitter in its ground state through a graphene nanosheet is investigated. The graphene plasmons (GPs) field distribution, especially the opposite orientations of the vertical electric field components on the two sides of the graphene nanosheet, produces a significant nonadiabatic process during the interaction between the emitter and the localized GPs. By taking into account the counterrotating terms, the excitation of the quantum emitter with simultaneous emission of a GP has a large probability. This happens for emitter speeds of about 10^{-4} times the speed of light. For accelerated emitters, the GPs exhibit thermal field photon distribution with a high temperature. As a consequence, this study provides a promising platform to observe the dynamical Casimir effect as well as a simulation of the Unruh effect.