Summary form only given. In order to improve the speed of microdisk lasers, the carrier diffusion process must be eliminated. Very recently, lasing has been achieved in InAs quantum dot (QD) embedded microdisk cavities. We report our experimental study of the dynamic response of microdisk lasers with quantum dots as the active media. In a QD microdisk laser, the carrier diffusion in the disk plane is suppressed because the carriers are confined in individual quantum dots. Hence, the turn-on time of a QD microdisk laser is greatly shortened, e.g., it can be as short as 7.8 ps at 5 K. Furthermore, we observed that the turn-on time increases as the pump power approaches the lasing threshold. This phenomenon is not easy to be observed in a QW microdisk laser due to carrier diffusion effect. The dynamics of the QD microdisk lasers has also been studied over a wide temperature range from 5 to 120 K. Under the same pumping level, the turn-on time appears to decrease with increasing temperature. This behavior may be a result of faster carrier capture and relaxation processes in quantum dots at higher temperatures.