I have no experience with buddy heaters. But I would not chance using that type with a new baby. The burning flame with no exhaust requires the right amount of fresh air and I really don't know what that amount is.
This is something you prepare for so I hope you didn't mean your leaving this weekend. If so, my advice is too late. Best thing you can do is take trailer to professional RV dealer and explain that you need your furnace fully inspected and repaired to provide safe heat for you and your family-- one of which is new baby. So fix it good, vent it good, replace it if it makes sense.
In our trailer I keep brand new batteries in the smoke alarm, the carbon monoxide detector, and the propane detector (well it's hard wired but new). Yes, 3 different devices in 3 separate locations. i hope it is enough...
This is important, good luck.