Piaget offered his hierarchy of childhood development, of which many of us are aware: pre-operational, concrete operational and formal operational thinking, and he gave us general age distinctions, plus or minus a year or so, within which he contended these levels of development occurred. I have an idea or two of my own.
Children, I believe, are not constrained by the conventions we as adults are compelled to adhere to. They do not suffer from fear of rejection, because up until they are kicked out of the nest, they are the center of their universe. Or pretty much so. The humorist and show host, Art Linkletter, used to say: kids say the darndest things. And they do.
Innocence breeds honesty, and inasmuch as their minds are not occupied with the worries and responsibilities of adulthood, they are free to wander and muse upon ideas, feelings and such that their parents have long since forgotten---or put away for future reference. Many of us have done that. Natural philosophers? Sure they are. They have the advantage of age. And we thought we had all the fun. The gift is tentative, though---for very many of them it will go away---just as it did for very many of us.

And for some of us---it comes back. Later. After we no longer need be concerned with the cares and worries of adulthood,---keeping a job we hated; pleasing a boss we could not help but disrespect. Or, at best, dislike intensely. No, philosophy has been approached in differing ways---mosty as an adult pursuit. I applaud your post regarding children as philosophers. Very astute, and somehow timely, given the season, which is and ought to be for kids anyway. There are other things that suit children for philosophy. But, I won't hog the show. Comments, anyone?

Before our childrens' minds are clouded by theories and faiths, they see only the simple truth.
If you look close you'll see the light in their eyes.
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KIDS AS PHILOSOPHERS
Thanks for these two provocative comments, which show that eventhough what "doing philosophy" means doesn't change with age, the outcome of the practice may be influenced by age.
If philosophy is the rational contemplation of thoughts (my def.), when do kids develop this ability?
First, when do they develop rationality?
Kids all can think (however you define it) almost (?) at birth, indicated by observing them, looking to see if their behaviour suggests intentionality. The behaviour could be called instinctive at first, but then as the behaviour is repeated to some desired end, it can be called intentional.
When does thinking become rational? When the child's thoughts become confirmed as leading to a result which the observing philosopher decides is desireable, thereby recognizing rationality of the child.
The child too, like all of us, seeks confirmation of what it believes. "Belief" is probably closer to the thought process of children than is scientific deduction at this stage. And we all have an "instinct" for the desire for confirmation of what we believe. "Rational" is what we philosophers call the child's thinking at this point; the child regards it as rational when it produces, or suggests it would produce, the desired result (one kind of confirmation).
For thought to be "philosophical," it must be confirmed in some additional way.
How is the child's philosophical thinking confirmed? Usually by finding co-incidence with the social group most influential and seen to be most successful, as the child defines success. And what a good example of philosophical thinking is "defining success," for instance?
So, when do children develop the ability to rationally contemplate thought? When they have had some threshhold experience of the connection between thinking and result, and when the desireability and success, in the child's view, of the conclusions about the thoughts, are confirmed.
Why was that child acting up and crying and screaming in the coffeehouse yesterday? Is he in physical pain; is he hungry or thirsty? No; he is behaving in some way that he knows is successful to some end he desires, confirmed either by his own past use of the behaviour, and/or by his observation of other people in his society successfully using it.

Good comments and perspectives from all thus far. My compliments and congratulations. Kids are consumate experts at mimicry and they know the best and worst ways of gaining attention and getting what they want. We, as adults, have to know when to reward; when to encourage; and when to say no. Unfortunately, an overly permissive society is making this much harder, transforming inquisitive accolytes into calculating manipulators. Yes, I believe parents might get some pointers from reading and absorbing Piaget's work---if they would take the time and have the courage to do so.
Just one person's opinion, though...

I guess I would classify as a "child". I am twelve years old and I have an interest in philosophy. As you stated earlier children do not always think rationally. I believe that that alone enables us to view philosophical issues with a different and occasionally better solution.
Your thoughts?

I remember Piaget from studying to be a teacher. I don't know of anything that has really overturned his work in all the intervening years.
AJUthinker noted that "children do not always think rationally." One of course should define what it is to "think rationally." People (including adults speaking to or about children) often use it to mean "think like I do." Slightly better is to define it as something like "is reasonable" or "thinks in a way that stands to reason." Reason, though, is just a tool. The best definition I know of is "recognizes cause and effect."
By that last definition, children indeed do not always think rationally. Neither do adults. Neither do philosophers always. So think on, and don't worry too much about "rationality." Great discoveries in almost every field, especially philosophy, are often intuitive leaps - we fill in the rational parts of the path after having glimpsed the destination.