Is there a specific reason for using N channel mosfet as a crude p channel?
How is it using the N-channel MOSFET as a P-channel? It uses a technique called bootstrapping, which allows an N-channel MOSFET to switch the high side, which is very common for motor drivers. When the MOSFET is off, C1 charges via D1 and the LEDs. When it turns on, D1 prevents C1 from discharging through the MOSFET and powers the oscillator circuit, whilst it's on. The MOSFET's source sits close to +12V. When Q1 turns off, C1 charges again.
I'd personally just utilize a P channel/PNP or a npn with a resistor from the collector to VCC, with the output from the collector.
Please post a schematic. Note the high side needs to be switched, rather than the low side. P-channel/PNP will definitely work. If bootstrapping isn't used, NPN would need to be an emitter follower, which will drop more voltage, but will probably work.