External cavity semiconductor lasers with strong optical feedback already exist using a gain chip medium. Owing to their ultrafast carrier dynamics, strong output power, and high temperature reliability, quantum dots as a gain medium are now envisioned as a promising solution to replace the current quantum well technology. This paper presents a semi-analytical rate equation model which is used to describe a quantum dot gain chip capable of lasing only with a free space external cavity laser. It investigates the evolution of the dynamical properties such as the turn-on delay and the damping rate. It also confirms the model's validity through the relative intensity noise and the frequency noise with respect to both material and device parameters like the linewidth enhancement factor, the gain compression factor, or the cavity length. Overall, this numerical investigation provides initial building blocks for future fabrication research and development of high performance devices including filters or gratings as wavelength-selective components.