OP, I am with your vet on this one. It sounds like she has had the same issues for some time and no one noticed them. I am a bit surprised because the head bobbing would be a clue for a vet to suspect a neuro issue....unless I have misread this and this is a new thing.
Unless I am reading this wrong, I would definitely not rush to do anything. You have time to get her properly diagnosed and come up with a plan. Just handle her with kid gloves...sounds like you already do that.