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This paper investigates the prescribed-time output feedback stabilization problem for a class of nonlinear time-delay systems. First, a novel dual-gain function is put forward by exploiting the dynamic gain and the time-varying gain function to design the reduced-order observer for reconstructing unavailable states. Then, by utilizing the Lyapunov--Krasovskii functional and state variables of the reduced-order observer, a new prescribed-time controller is presented based on the nonscaling design framework. Since no state scaling is required in controller design process under this framework, our control strategy is simpler and can greatly reduce the computational burden. Further, compared with the previous prescribed-time stabilization results, our designed controller acts on the entire time domain, not just a limited time interval. Based on our proposed stability criterion, it is proved that the controller can render that all system state variables converge to the origin within the prescribed time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]