We report on the design, the fabrication, and the optical characterization of AlGaAs microdisks suspended on a GaAs pedestal, conceived for second-harmonic generation with a pump in the third telecom window. We discuss the results concerning the linear characterization of whispering gallery modes at fundamental and second-harmonic wavelengths, an essential step prior to the investigation of quasi-phase-matched processes in this type of microcavity.