I would say to absolutely NOT use a propane burner inside. There are tags on the burner and the propane tank saying to not do it either. (not that many people pay attention to those tags, but still)
There are way too many horror stories I've heard about that sort of thing.
I would say that if you have to brew inside, go with either electric with a heat stick (or build your own based around a hot water tank element) or look into induction burners.
I just read about those the other day and I'm seriously considering going that route if / when I get a space to brew in, if I can't arrange a natural gas setup (complete with exhaust hood directly over it.)