Kids – most climbers agree, all kids should wear helmets!
Adults – Read the ‘Indoors – Adults Helmets’ post
Factors to consider…
What are the risks?
How valuable is Your Kids Head?
What do the Majority of other young climbers in your area do?
There are NOT many kids helmets on the market.
Measure your kids head and find out from the supplier what is the minimum size the helmet will fit.
Here are my opinions…
Indoor Climbing Helmets for Kids
Kids need to wear helmets until they are old enough and confident enough to ask not to wear one.
Indoor climbing is a much safer activity than outdoor climbing and the chances something will fall on your head are small. Be aware that climbing walls have to ensure to the best of there ability that everything you use is secure. Also remember you have to sign a waver form and guardian form for most indoor walls.
Side impacts are much more common on indoor walls. If the climber falls for any reason, the swing effect of being tied to a rope can pull you in any direction, including towards the wall. Ive bumped my head a few times this way and only once did i draw blood.
Using helmets indoors can help you get used to the extra weight you will experience when you climb outdoors.
in conclusion, any head gear that can absorb an impact is good enough to use on an indoor wall.
I hope you found this helpful 
Clive