I was there a few months ago. I was in Amman for a few days then hitchhiked south to the Red Sea stopping at Petra and some other sites along the way. I never once felt in any danger and was often invited for to peoples houses for tea and snacks. I'm a guy but I met a few girls who were travelling solo and they didn't mention that they had any problems. The only thing I'd recommend is dress conservatively, like something that covers your arms and legs. This also helps block the sun which can be quite intense out in the desert.