Your mosfet wan work fine with 3v3, assuming that you are not interested in fast switching (pwm etc) you can drive the mosfet directly.
Use a 100 ohm resistor from the pic to the gate , connect a resistor of 10k from the gate to the source, connect the source to the gnd and the drain as output to the load.
This will operate as a low side switch, your load will be connected to the positive supply and the mosfet will control the ground side of the load supply.
Alex