The N-Channel MOSFET that you have selected is listed as a "standard level MOSFET" in the title of the datasheet. This means that the gate drive voltage needed to turn on the device will be higher than a more specialized "logic level MOSFET". You should check out the transfer function charts in the data sheet to become familiar with the device characteristics. You will require a gate drive voltage (gate to source) of at least 5 Volts to achieve a decent level of drain current flow. In fact to achieve the advertised on resistance value of 4.6 mΩ you would require gate drive voltage of 10 Volts.
The gate driver IC that you have selected is not a particularly elegant part. Due to the emitter follower nature of the device the high (low) level output levels are a VBE voltage drop less than (more than) the input pin voltages. This means that if your microcontroller GPIO drive signals are a high drive of 5 Volts you would not see the output get to 5 Volts. In fact in the data sheet they state a typical value of 0.4V VBE when the current flow is 1uA. So even if you get the gate capacitance of the MOSFET fully charged the drive voltage can only get to around 4.6 Volts.
This is hardly a good match for part selection even if your MCU has 5V swing GPIOs. If the MCU you are using has 3.3V GPIOs (which is much more common) you have a non-starter solution here.
Further consider that if you do choose to use the R1 and R2 resistors as shown in your diagram they act as a voltage divider which will further reduce the gate drive voltage.