Hello and Welcome
As Selma said, you will find a wealth of information from other moms here that have been through it. I agree that if she already has a syrinx then something will have to be done about it. Did anyone comment on whether the incident with the dog could have caused the syrinx? I have heard that injury can sometimes cause one too and it sounds like she fell pretty hard.
For kids, from what I have seen the symptoms are pretty much like us adults experience but they sometimes have a harder time expressing them.
Here is a link of the more common symptoms from our health pages:
http://www.medhelp.org/health_pages/Neurological-Disorders/List-Of-Chiari-Symptoms/show/1024?cid=186
I got the same answers about it being genetic but I have seen so many families that have more than one member with it that it is just too coincidental to not be hereditary. I would go and get that MRI if you can.
Good luck and I am so sorry that you are going through this with your daughter...I have 3 boys and can only imagine how tough it would be.
Take care
Carolyn