Thanks for using the forum. I am happy to address your questions, and my answer will be based on the information you provided here. Please make sure you recognize that this forum is for educational purposes only, and it does not substitute for a formal office visit with your doctor.
Without the ability to examine your daughter and obtain a history, I can not tell you what the exact cause of her cerebellar atrophy is nor what her prognosis is. However I will try to provide you with some useful information.
The cerebellum is one of the structures in the brain involved in coordination (among other things). There are several causes of cerebellar atrophy Below, a few causes will be discussed but this list is by no means comprehensive.
In general, cerebellar atrophy could be divided into a few groups (1) those with a known external cause such as alcoholism or other medications or drugs (2) those that occur following infection (3) those that are neurodegenerative, due to loss of cerebellar cells because of a primary abnormality in cerebellar cells as opposed to an external cause such as infection (4) due to an inborn error metabolism and/or a genetic defect that disrupts metabolism in cerebellar cells (5) those that occur in the setting of cancer, known as "paraneoplastic ataxias" (uncommon in children), and (6) others
For the inborn errors of metabolism, some treatable examples include betalipoproteinemia, adrenomyeloneuropathy, cerebrotendinous xanthomatosis, familial vitamin E deficiency, maple syrup urine disease, pyruvate dehydrogenase deficiency, Refsum disease, and Wilson disease. Management typically relies on dietary modification, vitamin/cofactor supplementation, or drugs to reduce the load of the accumulating toxic metabolite, or removal of abnormal proteins from the blood by a procedure called plasmapharesis.
Other types of cerebellar atrophy that are genetic such as the large group of genetic disorders called "spino-cerebellar ataxias", Ataxia-telangiectasia, Friedreich ataxia, and other mitochondrial disorders are being studied, certain modifications may be helpful but there is not a cure. There are genetic tests available for many of these.
I recommend your daughter be evaluated by a pediatric neurologist, with referral to a geneticist or pediatric metabolic disorder specialist as indicated.
Thank you for giving me the opportunity to answer your question. I hope you find this information useful, good luck.