I have six kids between 13 and 40, was a range master with the boy scouts for many years and can tell you from experience that age 7 is not too young for a child to properly learn how to shoot. OTOH, as others have already said it really depends on the maturity of the individual child. There are many children who have more maturity at the age of 10 than many adults have at the age of 40. Still, a child is a child and despite what they may say or we may think as a doting parent, they are NOT miniature adults and need to be treated as children until they are of an age when they can be on their own and held responsible for their actions. It ALSO depends on the maturity of the adult doing the supervision! An adult is responsible for the safety of all children under his/her care, period. Whether at the gun range or the playground, you need to pay attention to the kids at all times. If you see a safety infraction you need to point it out immediately and ENSURE you are up to date and practice proper range procedures yourself.
Shooting MUST be done in a safe and responsible manner for the benefit of everyone present, but it should also be educational and fun! Kids (and adults) need to learn the importance of following established safety and handling rules, but that doesn't mean if has to be in a draconian, in your face, zero tolerance manner.
"... Americans... we want a safe home, to keep the money we make and shoot bad guys." -- Denny Crane