Due to the features of on-demand deployment and flexible observation, unmanned aerial vehicles (UAVs) are considered as one of the key enabling techniques for the next-generation sensing systems. Compared to a single UAV with limited sensing coverage and communication capability, multi-UAV cooperation is able to provide more effective sensing and transmission (S&T) services. Nevertheless, most existing works on multi-UAV sensing mainly focus on mutually exclusive task allocation and independent data transmission, which did not fully exploit the benefit of multi-UAV cooperation. Motivated by this, we propose a novel multi-UAV cooperative S&T scheme with replicated task allocation. Although replicated tasks may sound counter-intuitive, they can actually foster cooperative transmission among multiple UAVs and thus reduce the overall mission completion time. To minimize the mission completion time, task allocation and transmit power are jointly optimized. The considered problem is transformed into a monotonic optimization and solved by decoupling the variables of transmission time and power. Finally, simulation results demonstrate that the proposed scheme significantly reduces the mission completion time over benchmark schemes.