Biggest issue with gas work is not the permit or the inspection, it’s the pressure test. You have to shut off all appliances, using shutoff valves located before the appliances, hook up the gauge to the line, leave it pressurized for 24 hours (with air!), and have the inspector verify. It’s a royal pain in the neck for the homeowner.
You may be able to talk the building department into doing the inspection without the pressure test.
Were it me, I would just do it without the permit.