We have developed and experimentally demonstrated a novel monolithic InAs/InP quantum-dash dual-wavelength distributed feedback (QD DW-DFB) C-band laser as a compact optical beat source to generate millimeter-wave (MMW) signals. The device uses a common gain medium in a single cavity structure for simultaneous correlated and stable dual-mode lasing in the 1550-nm wavelength range. A record narrow optical linewidth down to 15.83 kHz and average relative intensity noise (RIN) as low as -158.3 dB/Hz from 10 MHz to 20 GHz are experimentally demonstrated for the two optical modes generated by the laser. As a result, the beat note between these two lasing modes generates spectrally pure MMW signals between 46 GHz and 48 GHz. Such an efficient, coherent, and compact optical source is extremely attractive for applications in MMW systems, such as Radar and fiber-wireless integrated fronthaul for 5G and beyond.