DD1 was tested by the school screening nurses in kindergarten and again in Yr1 cause there was a prob. She needed to see a paediatric opthalmologist after that and was prescribed glasses. The nurse advised us NOT to take a child to just an optometrist but go to the more qualified paediatric opthalmologist to get her eyes fully checked.

I have never heard that you should have their eyes tested by 3, as a teacher iw ill suggest an eye check for learning probs to rule it out as a casue but never just for the sake of it.