Very wise of you to ask!
I am very careful about my children,s health too!
Some advice that i would give applies to everybody really, but specially children.
A safe way to supplement is to make sure those supplements are natural and based around natural organic food products, or put simply,Plant based.
Store Bought, or "Naturally Inspired", products do not have the same effect and are considered harmful by some health professionals.
Using supplements made from food products are safer as this is a natural way of getting our supply of vitamins, minerals and phyto-nutrients, so Avoid Synthetic or Lab made copies, made for pennies.
The American medical Journals are recommending that everybody needs supplements, and i agree..take a look at my hub on Omega3.
Hope this has helped, do let me know...