Hi,
Certainly the diode (cathode) should NOT go to any PICaxe pin (which would be pulled to +12 volts and very probably "release the magic smoke").
As bill says, the diode is not strictly necessary for a purely resistive load such as an incandescent (filiament) lamp. But bear in mind that even the connecting wires have some inductance, so if they are "long" then the diode might still be beneficial (connected on the FET/circuit board, not near the lamp).
What is the purpose of the 100k ohm resistor? It only appears to be "leaking" about 120 uA out of the battery. Shouild it actually be on the gate to prevent the FET conducting if the PICaxe output is "off" (no power applied and/or output pin not switched as an output)?
Cheers, Alan.