We report a cavity-dumped 1123 nm laser with narrow pulse width and high peak power by an MgO: LN crystal electro-optic (EO) modulator. Based on the structural optimization design of a folded biconcave cavity using the 808 nm pulsed laser diode (LD) side-pumped ceramic Nd: YAG rod, output pulses with maximum pulse energy and peak power up to 39.6 mJ and 9.73 MW were obtained, corresponding to 100 Hz repetition rate and 4.07 ns pulse width. The instabilities of pulse width and pulse energy were $\pm$1.55% and $\pm$2.06%, respectively. At the highest repetition rate of 1 kHz, the pulse energy, pulse width, and peak power were 11.3 mJ, 5.05 ns, and 2.24 MW, respectively. The instabilities of pulse width and pulse energy were $\pm$2.65% and $\pm$3.47%, respectively.