AVR to drive 12V 1A motor
You should use a logic level gate MOSFET, not the IRFZ44N, which is not guaranteed to work.  Rds(on) is specified at Vgs = 10V not 5V. Vgs(th) is for 250uA. I think your motor needs more than 250uA. It would probably sort-of work badly if you try it. 

Connection is correct, however you must put a diode across the motor to keep the MOSFET from avalanching when it turns off. 

A 20K or 50K pull-down is a good idea- it keeps the transistor from turning on partially if the GPIO is high-impedance. 

A series 1K to the GPIO makes it a bit more foolproof. No other parts needed.