Wide band-gap materials, e.g., Silicon Carbide (SiC), allow the realization of power semiconductor with superior performance with respect to the traditional Si-based counterparts. On the other hand they require more stringent short-circuit or over-current clearing time to safeguard the device lifetime. This paper focuses on the analysis, design guidelines and practical implementation of a gate drive circuit incorporating fast short-circuit/over-current protection $(\lt 1 \mu \mathrm{s})$ based on the device di/dt measurement through PCB-based auxiliary Rogowski coils. The target power module is a industry standard 62mm packaged 1.2kV SiC MOSFET half-bridge. The gate driver protection features are experimentally tested and the target time for the short circuit clearing was satisfied, with the gate driver effectively turning off the switches within 400 ns during a short-circuit test.