I don't want mis-information to propagate here. Yes, you can run your trailer on a 15A circuit, with a few caveats...
First, you have to be aware of the AC loads you are putting on the system. You have the draws of different units.
Your converter will only draw 6+ amps when the battery is very low. As it charges up, the converter draw will decrease - eventually down to almost nothing.
Unless you are a very high power user of the RV, you'll be fine on 15 amps. Some can even run the AC, with nothing else running. (I've done it)
Worst case is you blow the breaker, and have to turn something off and reset it.
Electric heaters plugged in usually only draw ~12A when running on high. Leaving enough to run lights and other things, but not microwaves/AC/fridges/water heater.
Moral is, run the fridge/water heater on propane and have a great trip. All else should be good.