A P-MOSFET still requires +12V to turn-off, which may be a problem for the module.Why not use a Mosfet?
Not really, see post #6You still need a resistor between the IR output and the base.
You still need a resistor between the IR output and the base.
I think this is the schematic of the sensor (below), which uses a LM393 as noted by sghioto, that has an open-collector output:Not really, see post #6

That is correct. I have one of those sensors and originally thought the LED output indicator was on pin1.I think this is the schematic of the sensor
The relay is intended to be normally OFF.Is it intended that the relay be energised most of the time? or de-energised most of the time. What I see is that the IR sensor module is sinking a large amount of base current, probably exceeding the current rating.