Semiconductors require stable doping for applications in transistors, optoelectronics, and thermoelectrics. However, this has been challenging for two-dimensional (2D) materials, where existing approaches are either incompatible with conventional semiconductor processing or introduce time-dependent, hysteretic behavior. Here we show that low temperature (< 200$^circ$ C) sub-stoichiometric AlO$_x$ provides a stable n-doping layer for monolayer MoS$_2$, compatible with circuit integration. This approach achieves carrier densities > 2x10$^{13}$ 1/cm$^2$, sheet resistance as low as ~7 kOhm/sq, and good contact resistance ~480 Ohm.um in transistors from monolayer MoS$_2$ grown by chemical vapor deposition. We also reach record current density of nearly 700 uA/um (>110 MA/cm$^2$) in this three-atom-thick semiconductor while preserving transistor on/off current ratio > $10^6$. The maximum current is ultimately limited by self-heating and could exceed 1 mA/um with better device heat sinking. With their 0.1 nA/um off-current, such doped MoS$_2$ devices approach several low-power transistor metrics required by the international technology roadmap