Power Mosfet Gate drive current
The datasheet says:


  
  Features
  (2) Small gate charge: QSW = 30 nC (typ.)
  


With a constant current of 100 mA, this would result in a switching time of 300 ns. The current will not actually be constant, but this is much smaller than the smallest pulse width shown in the SOA graph, and probably safe for the VDS and ID values that your circuit uses: