It’s gas powered but can also use propane.
The extension cord is specifically for use with this generator.
Part of the caution with extension cords is that people don’t know what they are doing, and will put too “small” a cord on an appliance, and it will melt the insulation, exposing hot wire, and causing a fire. I have several times used higher-rated extension cords on things like free-standing, radiant heaters, but I know what I’m doing, since I was an military electrician, and I can look at the wattage, voltage, etc. of the heater, and choose an appropriate extension cord.
But there is also the issue of the fact the it is very easy to trip over cords, and first of all, hurt yourself, and second of all, partially unplug the cord, leaving a connection where it could arc, and cause a fire that way.
Also, the doggy door could be rubbing against the insulation, and causing it to wear away.
I would like to suggest that you use electrical tape to secure the place where the two cords are plugged together, and second, cut a corner off the dog door to create space for the cord, so it is not rubbing against anything when it goes through the door. If you want to insulate it, get a piece of Styrofoam, and cut it so it fits around the cord where it goes through the door, and wedges it in place.