First of all just a tidbit about the statue. There are plenty of tour guides there that will explain many of the facts about the statue. Such as; it was a gift from France and shipped in 350 pieces and took about 4 months to assembled.
Also, when visiting the Statue of Liberty with young children, strollers are not allowed in some areas and observatory. There is a Junior Ranger program available for children between ages 7 to 12 years old. Basically they learn about the statue with indoor and outdoor activities and the program takes about an hour. Be sure to give yourself plenty of time. The day visiting will take about 5 to 6 hours, and the ferry wait can take up to 2 hours during peak times. Another tip, bring a lunch. Waiting in line for food can take hours and use up your visiting time. There are picnic areas to eat a lunch. Lastly, look into getting a "Time Pass" in advance, online if possible. It allows you to skip some of the long ferry wait lines as well as entering the monument and other Ranger led areas. Look here to locate a "Time Pass" reservation: www.statuereservations.com, or call 1-866-STATUE4 for a reservation.