I have been playing World of Warcraft for almost 2 years, and my oldest daughter has finally taken an interest. She is 9 and is very bright for her age. She is more than capable of playing the game, and understanding the basic concepts mechanics. There are some great things you can do to make this game playable, and highly enjoyable for younger kids like my daughter. How do you accomplish this?
Keep the game sandboxed.
What I mean by this is, try and limit their playtime to areas that are nearly devoid of other players, and out of the huge chat channels with hundreds of people talking at once.
Choosing the correct "newbie zone" to level in is big. I find that the "BC" races, Draniei on alliance side, Blood Elves on the horde side, are best. Their starting areas are filled with rich quests and good low level loot, and will typically have very few other players around.
Also, having them work on tradeskills is a nice way to make the game a little more complicated for them, but also allowing their character to be self-sufficient. Make sure they pick skills that work for their class. For example, if they pick a mage..pick up tailoring and enchanting. If they start a Paladin, pick up mining and blacksmithing. This will allow them to gather materials while they play, and create their own items, which my daughter LOVES.
There are many other things you can do, like turning off the trade and general channels, and limiting your childs playtime.
Unsupervised however... this game is not a safe place for kids. There are unrestricted chat channels full of the kinds of chat the internet is known for, and highly addictive gameplay. Your kids will get sucked into this game, and love every minute of it.