When my son was in pre-K teachers encouraged us to get him to K without waiting for the age (pre-K is a not part of the elementary school). But we decided against it. Now my son is bored in Math and he is reading at the end of 3rd grade level while he is in 2nd grade. I do not know whether we missed the opportunity to get him at his level. we talked to his 2nd grade teacher and she agreed to give some challenging work for him. He is already in a reading group at his level. When we decided against skipping we thought of gaps and social issues. Our pediatrician warned us against skipping.
