P-channel is the right mosfet, not N-channel. When your NPN is turned off (Arduino output is low), then the pullup resistor on the mosfet gate raises the gate voltage to 6V, which turns off the mosfet. So your circuit should work.
What is the gate voltage when the NPN is off? If it is 6V, and the source voltage is also 6V, then the mosfet must be off. Are you sure you haven't reversed the drain and source? If they are reversed, then current would flow through the body diode even if the mosfet is off. The source should be connected to the 6V rail, and the drain connected to your load.