Pmclemore makes a good point. If you haven't used your Airstream recently, the gas lines have air in them. By starting the propane appliances the farthest away from the tanks, it purges the air from the lines and propane will flow to the other devices.
When we load up to leave, we start the stove and hot water heater and make sure they stay lit, to purge the air from the lines. Sometimes, this takes a couple of attempts, especially with the hot water heater, which has to be turned off for a few seconds and then back on again. Otherwise, the refrigerator has trouble starting (on propane). Not sure, but your stove is probably aft of your furnace, so lighting the stove will probable allow the furnace to start and run.