You didn't say what type of RV you have but propane furnaces in RVs consume a relatively high amount of both propane and battery power. I'll bet there are few longtime RVers here who haven't, at one time or another, run their batteries down while using their furnaces. Reading your post, it seems like you'll be boondocking. If that's the case, you might want to look into catalytic propane heaters. They only sip propane (one handheld disposable bottle will last an entire night) they're nearly silent, they do a good job of heating a room and they don't use any RV battery power. They're designed for RVs and safe to use indoors.
We've been using one for years. We keep a couple windows and vents cracked for airflow, and we've never had any of our CO detectors go off (Three motorhomes, 21 years). I plumbed ours to run off the RV's propane supply, and we've never had to refill our propane tank even once since we bought the RV 2 & 1/2 years ago. Like I said, they just sip propane. We're heading out tomorrow to an isolated Arizona camping area, and since the temps are only forecast to be in the low 40s at night, that's the only heater we'll use.
Kev