Recently single molecule photoemission statistics have been measured with a nanosecond time resolution for a pair of dye molecules attached to a DNA molecule and undergoing fluorescence resonance energy transfer (FRET) [Berglund, A. J.; Doherty, A. C.; Mabuchi, H. Phys. Rev. Lett. 2002, 89, 068101]. We have simulated single molecule photoemission in a model, where a FRET pair resides on a polypeptide molecule that undergoes diffusion in water, with the goal to understand how the dynamics of the molecule are reflected in the observed photoemission statistics. We further compare our simulation results with the classical theory of Haas and Steinberg [Haas, E.; Steinberg, I. Z. Biophys. J. 1984, 46, 429] and find that their approximation, while not quantitative in the case of fast diffusion in water, predicts well many of the qualitative features of the single molecule photoemission signal. The calculated second-order intensity autocorrelation functions exhibit photon antibunching at short times and photon bunching at longer times, the latter being crucially dependent on the time scales of intramolecular diffusion as well as on the properties of the FRET pair. Our study establishes potentially useful guidelines for the choice of FRET pairs for the experimental study of specific systems.