Am I calculating my shunt FET power dissipation correctly?
Power dissipation is \$I^2R\$ so 12mW, plus switching losses. I didn’t check how realistic your 100m\$\Omega\$ looks. It apparently is not guaranteed, so you’re rolling the dice. 

Note that average current is not as important as the average current squared (which is larger than the square of the average current if it’s switching at all).

Note that the switching speeds are specified with 1A peak gate current, so they are assuming a good gate driver. There is a lot of Miller capacitance in your situation due to the large change in Vds.