It's always scary to begin the design of a project with the statement "I believe...". Why not find the technical information for whatever you have, then you will have some values to begin you design with?
I believe the few facts presented to one in this case as a starting point.
Most videos / texts I've seen recently either show such low power lasers that they don't require switching, or they use purpose supplied drivers with built in PWM.
Even stated device specs are known to often be different to the wild. Some laser drivers are reported to paint out the chips... It appears most people buy a driver module and use that... But from looking I believe I may be able to Heath Robinson my own... Yet I am inexperienced, untrained and just starting to grasp these "things".
I'm simply after general advice from someone with experience of diode lasers (above 1000mW) and driving them correctly using Arduino. e.g.
High power laser diode assemblies usually provide feedback, either optical or thermal or both, so the driver can adjust the operating current dynamically to prevent burnout.
You certainly do risk destroying yours, if you don't pay very careful attention to the data sheet and design the driver accordingly.
I recommend checking the [manufacturer's website](http://NEJE MASTER Engraving Machine Carving Tool) for application details. There's probably already a MOSFET inside. You need to know the PWM voltage and you need to know how to measure the temperature output.
A bare laser diode has 3 pins. Power, ground, and feedback. The feedback tells the power supply to increase/decrease the current moment-to-moment to hold the light-output constant-correct and to help keep the laser from burning-up. I'm hoping all of that is built-into the module...
First I started by thinking LM7812 which can output 12V 1.5A
Maybe on a good day with a big heatsink when the stars are aligned... There is also a power (wattage) and thermal spec. Usually they overheat and shut-down before you hit the specified maximum current. What voltage are you feeding into the voltage regulator? The power dissipated (heat generated) in a linear regulator is Voltage x Current, where the voltage is the voltage dropped across the regulator.