You could feed a 12v through a buck converter (from the same 24v you power the Duet... Google about multiple voltage on Duet you'll see how to do that) to the V_FAN input and then plug the laser to one of PWM Fans output so you'd be able to power the laser from 12V on/off with a simple M106/M107 gcode.
Hope it helps.
You could use a software like Yawcam to get a static IP adress for your webcam (you can even choose a password to protect it). The software gives you 2 address (1 for a refreshing jpeg and 1 for a live feed of your webcam). That's what I use and I can check my print from anywhere, with the WebPanel or directly on a given webpage by the software.