I think that FET should do - at least the price is right. Turn-on resistance is a little high but no problem at only 1 amp load.
By the way, you don't put cr0sh's suggested filter into the feed to the FET driver circuit. This must only see the true PWM signal.
The filter is only used if you want to "convert" the PWM signal to an analogue value for display on a voltmeter.
You'd typically connect it into circuit by either tapping off a parallel feed from the arduino output pin or better still the FET output pin.