No, that is not a Logic Level MOSFET - all the switching times & currents are rated at 10V.
You want one with ratings at 4.5V.
The gate transistor is determined by the current flow you want out of the arduino.
Gate capacitance looks like a short to ground being charged up initially, or a fully charged cap being discharged.
If we limit the current to 35mA:
So 5V/35mA = 142.8 ohm, so a 150 ohm resistor would allow fast charging while not overstressing the IO pin.