Just got back from a 2-week trip to the Mideast, which included 8 days in syria with a friend, then another 6 days in Jordan on my own as a single female. It was an amazing experience, very highly recommended and I can assure you that I felt very safe travelling solo. I used the Visitjo.com Tour agency - www.visitjo.com - to arrange the Jordan part and then did Syria independently.
Happy to answer any questions about hotels, logistics, costs, etc. since I didn't get into that level of detail in my report . Enjoy!