I am sorry to hear about this. In such young children this is usually the congenital variant. It is caused by defects in the structure of brain and spinal cord, and occurs usually during fetal development. The cause is often a genetic mutation. At times it is due to lack of proper nutrients in the mother's diet. Usually the malformation is harmless, unless it is causing neurological signs. In this case surgery is performed to decompress.
I was diagnosed with Arnold-Chiari Malformation Type 1 at the age of 25, I'm 32 now..my 10 yr old was also diagnosed with borderline Chiari Malformation Type 1 and my cousin's son was diagnosed with Type III..I have never heard of any type of Chiari being because of the lack of proper nutrients in the mother's diet while pregnant, I have researched every site on the internet about this subject..and although they say that it can be passed down from generation to generation, there is still no cause..so NO, it is NOT your fault.