Colloidal semiconductor quantum dots (QDs) can be considered a promising material platform for solution-processed laser diodes. However, due to some fundamental challenges, the realization of electrically pumped lasing based on QDs remains unresolved. Here, a binary blend of QDs and ZnO nanocrystals is employed, which serve as nano-sized scatterers to facilitate waveguide gain in ultra-thin films. By carefully engineering the electric field in these films, an infrared amplified spontaneous emission in a record thin colloidal gain medium is observed, with a thickness of 16 nm, at a wavelength of 1675 nm. Employing these binary blends as a gain medium, an optically pumped infrared stimulated emission in a full-stacked light-emitting diode (LED) device is demonstrated. The functional LED device, which comprises a single layer of graphene as an anode electrode, shows strong electroluminescence under electrical injection. This study suggests a promising device for realizing infrared QD-based laser diodes.