No it will not damage the eye. Because the focus muscle is so strong in children (hers are three or four times as strong as yours) and because this muscle can cause the eyes to cross it is very important for pediatric ophthalmologist to use drops that last longer in adults. If you daughter is fair skinned and blue eyed they will make them last even longer.
Be sure you daughter is seeing a real physician Eye MD ophthalmologist. In my opinion pediataric patients that young should not be treated by optometrists.
Thank you, she is being seen by an MD ophthalmologist.
Next time in mention how long the drops lasted and they may be able to use a smaller dose or weaker drop.