Control 12v circuit from a Raspberry Pi
Yes, that should work, except that you can lose R1 since MOSFETs are voltage-controlled, not current controlled. Just make sure you get the drain-source polarity right, due to the parasitic diode. And since RPi GPIOs are push-pull outputs, you can probably lose R2 as well (although this will increase turn-off time and power usage just a bit).

The diode change is not a problem either, since the new diode will only have a higher voltage rating as its primary difference.