I am not sure if ds' experience is relevant but in case it helps in any way.
Ds was diagnosed at 18, literally a few weeks before his A level exams. He was struggling to focus during his revision, a fact he hid for years (is this masking?), even for GCSEs. Bright kid but it did not reliably translate to good grades. Now we know it is ADHD. Poor boy.
We went for a private diagnosis due to the urgency for the sole purpose of getting drugs. We had to find a psychiatrist who had availability at short notice. There was only one so we took it. We filled in some forms, got the school to fill in a form and 2 weeks later, had the assessment appointment. Ds got his diagnosis another 2 weeks later and was issued the drugs on the day itself.
So all in, it took 4 weeks and $800 for the diagnosis. I thought that was a really reasonable cost. The drugs cost about 100 pounds a month private, depending on strength of the dose. Subsequently, we got the GP to share care and now ds' drugs are free.
Although your dd may be new to the school, can her previous school fill in the form. One thing to ask the current school is whether they would rely on a private diagnosis to give your dd extra time in exams and a quiet space. All this is important for the mocks and A levels.
Medication has been transformational for ds. His self esteem was on the floor but now he has got his mojo back. He was able to focus on his revision and even enjoyed taking some of his papers. He is a changed boy. It is worth every penny to get the diagnosis and medication. We should have done it earlier.