OP, I would start with a therapist and go from there. This is really hindering her, and at 13, it is not a phase. It’s good you are trying to help with this instead of waiting to see.
This was posted in an old thread on dog phobias
This is a good book:
http://www.amazon.com/May-Pet-Your-Dog-How/dp/0618510346 You could read it together and then practice. It promotes safety, which is the key to feeling secure.
You might want to introduce him to a dog that is specially trained to be calm and well behaved. People Animals Love has a dog visiting program that includes several libraries:
http://www.peopleanimalslove.org/our_programs.php#petvisiting
Hero Dogs, a group that trains and places service dogs with veterans, also has many public events and appearances. These dogs are incredible. They're visiting the Gaithersburg Library in July:
https://www.z2systems.com/np/clients/herodogs/eventList.jsp