No. You need to level shift each gate drive as it needs to get all the way up to the respective supply rail to fully shut-off a P-MOSFET, so M2 will be hard on all the time (with min. -8.7V Vgs). Also the body diode of M1 wont block voltages above 5V (the rail feeding its source), so it will dump the 12V from M2 (less one diode drop) onto your 5V rail, letting out the magic smoke from the rest of your circuit.
To fix the level shifting issue, use low Vgs threshold N-MOSFETs to drive the P-MOSFET gates, with a pullup resistor to the P-MOSFET's supply rail. To fix the reverse conduction through M1 (via its body diode), add a schottky diode in series with M1's drain.
Does your buzzer actually work properly with 1K in series with it?