N., Thank you so much for your comments.
I wouldn't rush to give too much credits to the teacher or experts. I am probably considered an expert on my area but I know how much I don't know. In fact they always think they know everything about all the kids appear to be kind of arrgogant to me.
Also in theory the birth dates are distributed uniformly over the year in her class. But the fact is that most of the kids are way past 6 and some of the kids are even older than 7!! My daughter, not even six yet, with all the issues, would never stand a chance.
So my question is, do we have to have a specialist do a test? I just don't want to put her through that. She is old enough to know what's going on.