You can ask for an in depth eye checking at 健康院. I know that all babies should take development test at gov't health clinic when they are 1 year old, you can tell the nurse about your baby's situation, they will arrange your baby to see a doctor, then go for an indepth eye checking at hospital where eye checking for baby can be provided (as not all hospitals have such services). Of course, going for gov't hospital for eye checking requiries doctor's referral. You can try. Otherwise, private doctor consultation is required.