I actually had very complicated rules for this written out at one point for a first edition game which had been going on so long that the characters were having children.
I don't remember all of them, but here is an overview translated into 3rd edition.
In first edition, you couldn't gain a class level until at least one of your attributes was a 9. This percludes small children from being anything but 0 level, and is something that I think you'd want to keep doing even in 3rd edition. Most small children would start out as 0 level commoners - but I would allow them to switch out from commoner to 0 level anything else, or to first level anything else once they got some training.
You basically have to determine two attributes: attributes at maturity, and attributes at birth. Attributes at any point in between are assumed to be proportional to the time that has passed for the sake of simplicity. Attributes at maturity can be determined normally (I had a complex system for determining them based on the 'genetics' of the parents, their zodiological sign, and random chance). You may wish to modify the 'mature' stats by the young adult modifiers or other modifier.
Attributes at birth can be determined by assumption.
STR at birth is 1 for most humanoids.
DEX at birth is 1 for most humanoids.
CON at birth is 1/2 that of maturity.
INT at birth is 1 for most humanoids.
WIS at birth is 1 for most humanoids, and 1/2 maturity for feral ones. Feral is defined by the DM, but probably includes things such as Kobolds, Lizard Folk, Merfolk, and other humanoids needing survival skills of some degree from birth forward.
CHR at birth is 3/4 that of maturity.
Some people may quibble over the CHR, but I note that children can be quite charismatic, and that they are usually able to become quite skilled at skills that depend on charisma (bluff, perform, intimidate, etc.) Note also that intelligence is not strictly a measure of IQ, but also of general knowledge and experience.
At birth, humanoids tend to be two sizes smaller than at maturity and have the 'baby template'. After 1/4 of the time to maturity, they move up one size and have the 'child template', and after 3/4 of the time to maturity they move up to thier final size (and have the 'youth template'). Being small has its advantages, notably in ability to hide and apparant dexterity (the AC and attack bonus). Beings with the 'child template' also gain the extraordinary advantage 'Lithe' if they are small size or smaller, which has the following benifit: You gain a racial bonus (cumulative with other racial bonuses) to the skills balance, climb, escape artist, jump, and tumbling, equal to your attack bonus due to size (for example +1 for small creatures).
As I said before children should probably not be classed until they have at least a 9 in one attribute other than CON, and should probably not be 1st level before maturity unless they grow up in an environment in which they recieve unusually intence training (Paul Atredies for example). First edition had prime requisites. For this purpose alone I'd bring them back. Skills should be proportional in time to the point when they first gain a 9 other than in CON or reach maturity (which ever comes first), and unless a child has recieved unusually intence training they should probably have half normal skills.
Maturity should be determined randomly. Probably for humans, 1d4+12 should be fine for females and 1d6+13 for males. Maturity here does not mean emotional maturity of course.

However, I do believe that in general a 15 year old has almost all if not all of the capacity of an adult it is just usually untapped.
As to what sort of campaign you would run for an all child cast; why you would run fairy tales of course!
