Maybe, sort of. Looks to me like it won't work that well. In particular, it might give more like 2A, (well if the particular MOSFET happens to have a low \$V_T\$, otherwise it won't be regulating via Q1 at all).

I'd increase the gate protection zener to 12V 500mW, use a regular BJT for Q1 rather than a Darlington, and start off with a higher value for R2 (around 0.65 ohms 1W or 2W).

Maybe, sort of. Looks to me like it won't work that well. In particular, it might give more like 2A, (well if the particular MOSFET happens to have a low \$V_T\$, otherwise it won't be regulating via Q1 at all).

I'd increase the gate protection zener to 12V 500mW, use a regular BJT for Q1 rather than a Darlington, and start off with a higher value for R2 (around 0.65 ohms 1W or 2W).

Edit: I'm not kidding about increasing the gate protection zener. A 4.7V 1300mW zener might only allow 3.5 or 4V at tens of uA. Subtract 1.x volts for the Darlington and you're left with less than 2.5-3V for a MOSFET that requires 2-4V (that's what my reference above to \$V_T\$, is alluding to) in order to pass a mere 0.25mA. It really needs to be able to see about 6V between gate and source to assure 1A output current, meaning more than 7V referred to ground.