There are import provisions for every pet from so-called non-listed third countries, syria is included.
Their owners have to proove, that for example the dog carried with them is theirs. For that they need a special pet passport, which you get when you get your dog chipped with a microchip. If you don't have such a passport, you need to get in contact with a boundary-veterinarian as soon as you arrive in germany. These places are listed here: http://www.bmel.de/DE/Tier/HausUndZootiere/Heimtiere/_Texte/HeimtiereEinreiseregelung.html#Liste
Please do that as soon as possible, otherwise it can't be guaranteed that your pet will stay in germany (or austria or wherever you want to be) or worst cases: it will be sent back to your homeland or, if thats not possible, put to death.
We made a list with import provisions, sadly its just a german version.