Do the math. Find the total effective gate capacitance of the FET. Determine the maximum rate you will ever switch the FET. From that you can get the average current required on from the 12 V supply. If that's more than 84 mA, then you chose inappropriate parts.
If less than 84 mA, then it is doable. Find the total charge that is required to drive the get high once. Assume all that charge will come from the cap across the power input of the gate driver. Use a capacitance large enough so that the voltage drop is acceptable.
Once you do all that, you'll realize that you don't really need much. Then just plunk down a 1 µF 20 V cap and be done with it.
I just looked at the FET datasheet, and the total effective gate charge is 200 nC. That will cause a drop of 200 mV on a 1 µF cap. That shouldn't be a problem. If you don't like that for some reason, put a 10 µF cap in parallel with the 1 µF. In that case, put the 1 µF physicall closest to the gate driver IC.