If you go to a neurologist you should still make sure they work with autistic people, because I had to go to a neurologist once (before I was "officially" diagnosed, in the midst of diagnosis, and I did not mention it to him because I felt uncomfortable self-diagnosing). I doubt he knew the first thing about autism; he just tested me for signs of a brain tumor and/or stroke. He also suggested I might look into electroshock therapy again based on my reactions/behavior in his office (I had been recommended electroshock at one point).
I was diagnosed by a psychologist who was familiar with it, and she has even said in my reports that I probably don't need therapy or medication, because history has proven (for me) they tend to create more problems than they solve. I think it would depend far more on the experience and generally outlook of the clinician way more than their official title (neurologist, neuropsychologist, psychologist, psychiatrist, etc.)