We designed AlGaAs-on-aluminium-oxide all-dielectric nanoantennas with magnetic dipole resonance at near-infrared wavelengths. These devices, shaped as cylinders of 400nm height and different radii, offer a few crucial advantages with respect to the silicon-on-insulator platform for operation around 1.55μm wavelength: absence of two-photon absorption, high χ((2)) nonlinearity, and the perspective of a monolithic integration with a laser. We analyzed volume χ((2)) nonlinear effects associated to a magnetic dipole resonance in these nanoantennas, and we predict second-harmonic generation exceeding 10(-3) efficiency with 1GW/cm(2) of pump intensity.