Wavelength conversion technology is imperative for the future high-speed all-optical network. Nonlinear four-wave mixing (FWM) has been used to demonstrate such functionality in various integrated platforms because of their potential for the realization of a chip-scale, fully integrated wavelength converter. Until now, waveguide-based wavelength conversion on a chip requires a pump power beyond the reach of available on-chip lasers. Although high-quality factor (Q) microresonators can be utilized to enhance the FWM efficiency, their narrow resonance linewidths severely limit the maximal data rate in wavelength conversion. In this work, combining the ultrahigh effective nonlinearity from a high-confinement aluminum gallium arsenide waveguide and field enhancement from a microring resonator with a broad resonance linewidth, we realize all-optical wavelength conversion of a 10-Gbaud data signal by using a pump power, for the first time, at a submilliwatt level. With such a low operation power requirement, a fully integrated high-speed wavelength converter is envisioned for the future all-optical network. The waveguide cross-sectional dimension is engineered in a submicron scale to enhance the light confinement, which pushes the device effective nonlinearity to 720 W-1 m-1 while maintaining a broad operation bandwidth covering the telecom S-, C-, and L-bands. Moreover, we demonstrate that a single microring resonator is capable of handling a high-speed data signal at a baud rate up to 40 Gbit/s. All the wavelength conversion experiments are validated with bit-error rate measurements.