First and foremost, I'd get the furnace fixed, or replace it with a vented Platinum Cat, as suggested previously. Combustion gases belong on the outside of your rig, and not where you breathe them.
Yes, a Buddy heater is a decent heat source. I used one when tent camping. It worked well, and because of the large rainfly, which made it fairly drafty, ventilation wasn't a problem, and it sat on an aluminum table, so a fire hazard was minimized.
There are four important caveats with a Buddy heater:
1: Even though the backside and bottom side are cool, the front and above it can get hot. In a RV, it really needs to be combined with a fan blowing above it (not directly on the heater, since it would blow the pilot out, but above it to circulate the warm air.) The Big Buddy heater has a fan built in, and that can use batteries or with an adapter, A/C power. At the front, it can easily catch bedding on fire if stuff comes in contact.
2: If you use the 1 pound propane bottles, you will wake up in the middle of the night freezing when they run out. Learned this firsthand. Low setting lasts about 4-6 hours, high, about 2-3, and the regular sized Buddy will need to be run on high to keep a typical RV warm.
You can hook the Buddy heater to a propane hose. Now comes the tough choice. Some people are able to tee off their RV's propane system safely and have the Buddy heater use that. However, this should be done by an expert, since it does require a fuel petcock (so one can disconnect the Buddy heater and still use the stove, fridge, water heater, etc.) You can also run a propane hose directly to a bigger propane cylinder. However, one has to find a way to locate the cylinder outside for safety's sake.
3: Burning propane makes a lot of water vapor. In a closed RV, this can cause problems over time, maybe even water damage.
4: There is the issue of ventilation. This is a tough one because too little ventilation is dangerous, too much can wind up venting the precious warm air outside.
There is nothing dangerous about a Buddy heater if basic guidelines (which are spelled out in its owner's manual) are followed. I keep one, but it is something used as a last resort, where my propane furnace, and a generator and electric heater are either broken or can't be used (out of fuel.)