Although its not good design practice to use an OPAMP as a comparator, I don't think the OPAMP can get itself in any trouble driving an IRF830 MOSFET gate.
* The circuit has over 4% hysteresis, which with the likely supply voltage in the 10 to 15V region, is over half a volt , so its extremely unlikely that it could ever rapidly pulse between on and off at a rate fast enough that the dissipation due to charging/discharging the gate capacitance could be significant.
* The LM358 has a slew rate of about 0.5V/us and is good for about 40mA of output current (subject to dissipation constraints). The IRF 830 has 38nC worst case total gate charge, with a turn-on plateau of about 12nC. The OPAMP cant actually slew fast enough outside the plateau region to drive 40mA into the gate, and worst case, assuming entering the plateau region at 0mA output current and ramping up to 40mA at the end of the plateau charging time, gives a duration of 0.6us during which time the voltage across the gate resistor, limited by the slew rate cant exceed 0.3V. That means the resistor could be as low as 10 ohms and the peak current would still be under 40mA.
* The LM358 output current is internally limited and its short-circuit tolerant, subject to dissipation constraints.
* 100 ohms in series with the gate should be sufficient to prevent RF oscillation as the MOSFET passes through its linear region (though it would be advisable tp locate the resistor close to the gate pin.
0xfede's suggestion to add some series resistance to the LDR+trimmer potential divider to prevent damage if the trimmer is set to minimum and the LDR is brightly illuminated is good. A total of 570 ohms would keep the LDR dissipation under 0.1W at up to 15V supply voltage. It only needs one 680R resistor in series with the pot unless you need to be able to set the switching point for very bright illumination, in which case a pair of 330R resistors one in series with the LDR and the other with the pot would be preferable. That should be safe for any ORP12 clone. If you are using a miniature LDR, consult its datasheet for actual dissipation and current limits and recalculate the minimum resistance accordingly.
A 10K gate pull-down is pointless - the OPAMP has a push-pull output stage and no strobe pin so its output can never go Hi-Z.
Although the IRF830 is rated for repetitive avalanche operation, it would be advisable to add a reverse biassed diode across the main load terminals to shunt the back-EMF if long cables or an inductive load are ever connected.