It'd be a pretty fair assumption to say that ANSI keyways (3/32 in this case) are designed to for nearly maxmimum torque transferring power (not maximum because they are designed so the key breaks first when everything is the same material). You can do some pretty simple shear strength calculations to figure out exactly how much torque you can transfer. I did half of it for you just because I was curious
13 Nm = 9.6 ft-lb
9.6 * 12 = 115 in-lb
115 / ((3/8)/2) = 614 lb of force shearing the key