I don't know what is your budget like. If budget is an issue you can always get a GP to write you a letter to KK or National Eye Centre.
But personally, I know of one that is very good - she will take the extra time and effort to connect with your child, and the parent, and not just going through the tests. However, she is not cheap! My mom's eye test for cataract and gloucoma (first consultation) came up to $1k. My daughter saw her for styes problem, and that first consultation came up to $400. She was 4 when she saw the doctor, and her whole team just treat her like a princess. So she loved going there, even though they ended up having to do a surgery for her!
PM me if you are interested.
