To access the wavelength within the 1.1-1.3 μm region, we have developed a quantum-dot (QD) laser with an external-cavity configuration and a linewidth of kilohertz at a 1 ms integration time. The residual electroluminescence, due to the inhomogeneous broadening of the QD gain medium, was observed and filtered out using a grating. While a fiber-coupled electro-optical modulator was employed, this laser system was locked to a high-finesse (F∼18,500) optical cavity, and noise-immune cavity-enhanced optical heterodyne molecular spectroscopy was used to observe weak transitions. The Doppler-broadened spectra of a weak N(2)O transition at 1.283 μm are obtained with a signal-to-noise ratio of 30 for a gas pressure of 54 mTorr. The minimum noise-equivalent absorption coefficient is 5.3×10(-10) cm(-1) Hz(-1/2). This system can be a powerful and stable light source for atomic parity nonconservation measurements using thallium, ytterbium, lead, and iodine.