We investigate the impact of short optical feedback on a two-state quantum dot laser. A region in the feedback parameter space is identified, where the laser emission periodically alternates between oscillation bursts from the quantum dot ground and excited state, i.e. two-color anti-phase oscillation bursts. We compare these results to the low-frequency fluctuations and regular pulse packages of single-color semiconductor lasers and show via an in-depth bifurcation analysis, that the two-color oscillation bursts originate from a torus-bifurcation of a two-state periodic orbit. A cascade of further period-doubling bifurcations produces chaotic dynamics of the burst envelope. Our findings showcase the rich dynamics and complexity, which can be generated via the interaction of electronic and photonic time scales in quantum dot lasers with optical feedback.