Recent work has shown the Quantum Dot (QD) material system to be well-suited to support dual-mode lasing. In particular, optical injection from a master laser (ML) into the residual Fabry-Perot (FP) modes of a 1310 nm Quantum Dot Distributed Feedback (QD-DFB) laser has been recently demonstrated to offer a highly reliable platform for stable dual-mode lasing operation. External controls on the ML, such as operating temperature and bias current, can be used to precisely adjust the spacing between the two lasing modes. This tunability of modeseparation is very promising for a range of applications requiring the generation of microwave, millimeter wave and terahertz signals. Considering the versatility and utility of such a scheme, it is imperative to acquire a deeper understanding of the factors that influence the dual-mode lasing process, in order to optimize performance. Toward this end, this paper seeks to further our understanding of the optically-injected dual-mode lasing mechanism. For fixed values of optical power injected into each FP residual mode and wavelength detuning, the dual-mode lasing characteristics are analyzed with regard to important system parameters such as the position and the intensity of the injected residual mode (relative to the Bragg and the other residual FP modes of the device) for two similarly-fabricated QD-DFBs. Results indicate that for dual mode lasing spaced less than 5 nm apart, the relative intensity of the injected FP mode and intracavity noise levels are critical factors in determining dual mode lasing behavior. Insight into the dual-mode lasing characteristics could provide an important design guideline for the master and QD-DFB slave laser cavities.