Hi,
my DS saw a neurologist, attached to the Royal London in London.
He was lovely, and I felt like I could talk to him and trust him.
My DS's background - he wasn't responding to visual stimuli and was not smiling, so my GP referred him to a neurologist who referred him to an opthalmologist.
At the initial appt with the neurologist, he did a basic physical exam to test his reflexes and muscle tone. At the time we were told he didn't have an underlying neurological condition, but he was referred for an MRI.
For that, because he was so young (six months), he was anaesthetised with gas, but he was done within an hour and a half of having the anaesthetic, and apart from being a little sleepy for the rest of the day you wouldn't have known that anything had happened to him.
He went back to the neurologist two weeks later for the results of the MRI, and also another physical exam to check his eye movements and muscle tone (head control, etc).
He is going to be followed up again in six months.
It sounds like your DD's case is different to my DS's but I found it really reassuring dealing with the neurologist.
All the best,