The slowdown of optical pulses due to quantum-coherence effects is investigated theoretically for an "active material" consisting of InGaAs-based double quantum-dot molecules. These are designed to exhibit a long lived coherence between two electronic levels, which is an essential part of a quantum coherence scheme that makes use of electromagnetically-induced transparency effects to achieve group velocity slowdown. We apply a many-particle approach based on realistic semiconductor parameters that allows us to calculate the quantum-dot material dynamics including microscopic carrier scattering and polarisation dephasing dynamics. The group-velocity reduction is characterized in the frequency domain by a quasi-equilibrium slow-down factor and in the time domain by the probe-pulse slowdown obtained from a calculation of the spatio-temporal material dynamics coupled to the propagating optical field. The group-velocity slowdown in the quantum-dot molecule is shown to be substantially higher than what is achievable from similar transitions in typical InGaAs-based single quantum dots. The dependences of slowdown and shape of the propagating probe pulses on lattice temperature and drive intensities are investigated.