The ATtiny datasheet has a lot of useful information about power dissipation for its IO pins. The input capacitance of your MOSFET gate seems to negligibly effect the power usage compared to the 30 Ohm gate resistance. At 5.5V that's 183mA and above the 100mA supply limit, so you'd only actually need a minimum of a 25 Ohm resistor (+30Ohm gate) in series to lower it under 100mA (plus maybe add a heatsink depending on your duty cycle).
If you can handle supplying 100mA, then you'd get roughly a 60ns rise time based on the 1nF capacitance, which should be plenty fast for switching anything under 100kHz. This scales linearly, so selecting a resistance to target 10mA would give you a 600ns rise time (thus lowering the switching frequency you can hit before overheating the MOSFET).
