The high-speed modulation characteristics of an injection-locked quantum dot Fabry-Perot (FP) semiconductor laser operating at 1310-nm under strong injection are investigated experimentally with a focus on the enhancement of the modulation bandwidth. The coupled system consists of a directly-modulated Quantum Dot (QD) slave injected-locked by a distributed feedback (DFB) laser as the master. At particular injection strengths and zero detuning cases, a unique modulation response is observed that differs from the typical modulation response observed in injection-locked systems. This unique response is characterized by a rapid low-frequency rise along with a slow high-frequency roll-off that enhances the 3-dB bandwidth of the injection-locked system at the expense of losing modulation efficiency of about 20 dB at frequencies below 1 GHz. Such behavior has been previously observed both experimentally and theoretically in the high-frequency response characteristic of an injection-locked system using an externally-modulated master; however, the results shown here differ in that the slave laser is directly-modulated. The benefit of the observed response is that it takes advantage of the enhancement of the resonance frequency achieved through injection-locking without experiencing the low frequency dip that significantly limits the useful bandwidth in the conventional injection-locked response. The second benefit of this unique response is the improvement in the high frequency roll-off that extends the bandwidth. Finally a 3-dB bandwidth improvement of greater than 8 times compared to the free-running slave laser has been achieved.