To meet the requirements for simultaneous sensing and communication, full-duplex operation is essential for dual-functional radar-communication (DFRC) systems. In this letter, both the full-duplex self-interference cancellation (SIC) and the corresponding power allocation problem is studied for a pulsed DFRC system. First, a full-duplex design is provided, and the radar signal to interference-plus-noise ratio (SINR) and the communication rate are derived considering imperfect full-duplex SIC. Then, a max-min-ratio problem is formulated to maximize the radar SINR under the constraint of the communication rate. For time-invariant channels, a closed-form power allocation solution is derived for both radar and communication pulses. For time-variant channels, we provide an iterative solution by adopting quadratic transform and successive convex approximation (SCA). Simulation results are further given to verify the effectiveness of the proposed designs.