I don't have any experience with atlantoaxial luxation, but what the vet described as damage at the C1 and C2 vertebrae fits the description of atlantoaxial luxation. You should definitely call the vet back and see if that is the correct diagnosis. Searching on the internet will only worry you until you hear for sure from your vet. If that's the correct diagnosis, and if it's hereditary, surgery might be the way to go. If it was caused by an injury, there are more conservative nonsurgical treatments that might work. Here's a good article for those who haven't heard of this ailment:
https://vcahospitals.com/know-your-p...axial-luxation