My RV has a compartment designed for operating a generator. It has a small side door for exhaust and a front access door. The front door has a heavy mesh grate so I can lock the door and still keep the generator in use. At a minimum I would get a heavy lock and chain to deter theft if you take a walk and leave the door open.
My generator compartment is lined with heavy galvanized steel. If something goes wrong and I get a fire a wooden compartment would be risky. I would also avoid storing any flammable materials in the compartment. You could use the space to store extra gas and remove the cans before operating the generator.
