Note that this circuit is untested and designed by a non FET expert (that's me), do not bet the house on it.
With a VBAT of 6v that R1/R2 divider will produce approx 550mV on the Q1 gate. That's 5v45 lower than the Q1 source so you need a P-ch FET that will be turned on with a GVS(th) of say -5v. As Q1 is only driving a high-impedance input it doesn't have to turn on very hard, I would think most small FETs would do. I don't have much data on small FETs but something like the IRLML5203 seems appropriate.
where do I "kick-start" the regulator?
As Q2 turns Q1 on you need to emulate Q2. A switch across Q2 should work.
Note that VBAT should not be higher than 20v with the IRLML5203 (max VGS is 20v).