Hearing is one of the most important senses a human has and using special headphones for kids is something you should consider. The ear is one of the easiest senses to damage permanently. Children are especially vulnerable and even a short burst of high volume close to the ear can damage a child's hearing for life.
There are many headphones for kids on the market that are simple and cheap. The main aspect that you should be looking for in a headset for children is the volume limiting capacity. Be warned though that cheap products may be colorful and have cute design, but the audio components in this type of kid headphone are of very low quality. And low quality means you can never trust the performance. Bad audio can also be harmful in itself, regardless of volume because of the distortion. Even though the volume is not very high distorted audio can damage hearing permanently.
Kids want the most out everything and when they listen to music on the media player at home or in the car, you can be sure they will turn up the volume as much as they can. The cheap child headset you purchased may actually be doing the harm instead of protecting the hearing of your child.
Keep in mind that even though some products are marketed as Headphones for Kids the only thing related to children is actually the cheap price or the robustness of the unit. Very few of these products actually have real volume limiting capabilities. Most of these units have a volume control somewhere but this is not enough high sound protection for you kids ears because if you can use the volume control, so can they.
So what is a safe volume level for a child? Around 85 decibel is the established limit where you can allow your child to listen to music, or any other sound, for a longer time. If you have kids near you when you for example bring out the lawnmower, you are advised to make them wear noise isolating earmuffs.
You can find more information about quality headphones for kids and other child headgear and audio products at Kids Headphones.