N channel being better than P channel applies to the die area used, i.e., cost in high-power switching. Also relevant in making the Vdsmax * Rds(on) * Qg(tot) product better; again, for high power. Not relevant for your case.
For a 2.8V, 5mA load, justifying the extra complexity of the bootstrapped N-channel FET will be very hard. So, go for the P channel.
With 5mA load, it seems likely you won't have too much of capacitive load to charge, correct? I would guess the peak current won't cause an issue, so no need for active current limit / protection. So, again, bare P channel MOSFET.
Going even further, if Rds(on) varying between about 10-30 ohm as a function of everything is good enough for you, i.e., no accurate load regulation needed, directly power your load off the IO pin.
This is, assuming no large capacitive load, and assuming no short circuit will ever happen. If you are concerned about short circuits or precharging a large C, use a proper high-side switch IC with current limit and thermal protection.