We demonstrate the first silicon carbide (SiC) double-microdisk resonator (DMR). The device has a compact footprint with a radius of 24 μm and operates in the ITU high frequency range (3-30 MHz). We develop a multi-layer nanofabrication recipe that yields high optical quality (Q∼10) for the SiC DMR. Because of its strong optomechanical interaction, we observe the thermal-Brownian motions of mechanical modes in a SiC DMR directly at room temperature for the first time, to the best of our knowledge. The observed mechanical modes include fundamental/second-order common modes and fundamental differential (D1) modes. The D1 modes have high mechanical qualities >3800 at around 18.4 MHz tested in vacuum. We further show that optomechanical interactions, including linear and nonlinear optomechanical spring effects, can be observed in a SiC DMR at sub-milliwatt optical power. The SiC DMR has great potential for low-power optomechanical sensing applications in harsh environments.