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In this paper we theoretically investigate the statistical light-emission properties of an optically injected bimodal quantum-dot micropillar laser with high spontaneous emission rates. The nanostructured device is described in terms of a stochastic, semiclassically derived rate equation model. We focus on the stochastic switching dynamics between the two fundamental modes and correlate the results with an in-depth bifurcation analysis of the underlying deterministic dynamics. By analyzing different statistical measures, e.g. average intensity, auto- and cross-correlation functions, as well as dwell-time distributions, we give a road map on how to unravel the different dynamic regimes in the presence of large noise from experimentally accessible quantities.