Driving 3 LEDs at 1000mA. Is this circuit / driver ok?
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.