Fridge on when driving??

Use of propane while traveling isn't necessarily dangerous. Before our refrigerator died and I replaced it with an AC/DC model, I used propane while driving with no issues. I did put bug screens on the vents to keep wasps from building nests in the burner area (had that happen when we first bought the RPod). As to why it is beeping, you might wish to check to see if your refrigerator is operating on propane or battery. The beeping could be low battery or it could be that the flame failed to light. Do you have the propane turned on or off when you are on the road?

Like the others have said, I run my fridge almost exclusively on propane. Its very efficient and works well. Not so on 12v power, it runs the battery down quickly. So when I unplug from shore power, I always switch it to propane and let it run that way when travelling. 

I ran my fridge on 12V while on the road, not because I was concerned about propane safety but because it saves on propane and the tow vehicle alternator kept the batteries charged just fine. Also, I frequently passed through the Norfolk bridge tunnel, one of the several tunnels in the country that bans propane use.  Just remember to switch over to propane if you stop for more than a few minutes or your trailer battery will discharge rapidly. 

We also run the fridge on 12V. OK for us because our F150 turns off the 12V to the trailer when the engine is off. We switch to propane when we get to the final destination. We know a lot of people who just leave it on propane all the time, but for us, it's better to not have to think about it.

From what I understand, there may be a fuse that needs to be inserted in the fuse block for the connector to supply power to the trailer. Check your truck's owner's manual for details.