We report the fabrication and characterization of silicon carbide microdisks on top of silicon pillars suited for applications from near- to mid-infrared. We probe 10 μm diameter disks with different under-etching depths, from 4 μm down to 1.4 μm, fabricated by isotropic plasma etching and extract quality factors up to 8400 at telecom wavelength. Our geometry is suited to present high $Q$ single-mode operation. We experimentally demonstrate high-order whispering-gallery mode suppression while preserving the fundamental gallery mode and investigate some requirements for nonlinear optics applications on this platform, specifically in terms of quality factor and dispersion for Kerr frequency comb generation.