Its a MOSFET, so not much current is needed.
You're really just protecting the driver from the FET's input gate capacitance.
With 1590 pF input capacitance, not much protection is needed.
74LS138 can only source 0.4mA of current, so I would add pullup resistors to turn the FET off fast/
It can sink 8mA, so size the pullup to not exceed that.
5V/1K =5mA, should provide good performance.