What did the Xrays show? Damage in the spine could cause those symptoms and it might not be hips at all. My Lab girl was found to have invertebral disk disease and significant spinal spondylosis in about the middle of her back when she was 12.5. Her symptoms were similar though not nearly as bad as your dog, but her hips were excellent. We had her till she was 14.5 so I consider 9 to be fairly young.
If it was me I'd want a lot more detail from my Vet on WHY he/she is recommending a visit to a specialist. Maybe a second opinion from a different Vet is in order before you commit to the Neurologist.