Celebrim
Legend
Ultimate Campaign: Young Characters (pg 194-195)
From the Random Young Staring Ages table, footnote 1) During youth, +2 Dex, -2 to Str, Con and Wis
That might be suitable for a quick rough answer when you are in a rush and need something now, but it really doesn't go deep enough.
a) Does it suggest that 4 year olds, 8 year olds, and 12 year olds have the same capabilities?
b) Is a 6 year old or even a 12 year old as smart (on average) as an adult, keeping in mind that in D&D 'Intelligence' is also as much a measure of learning, experience, etc. as it is of cognitive power?
My methodology IIRC was to calculate the mature stats of the character and the age of maturity (say 16 in the case of human females, or 18 in the case of human males). I then applied the following rules:
STR/DEX/INT/WIS = Mature stats * Percentage of maturity obtained
CON/CHR = 1/2 Mature stats + 1/2 Mature stats * Percentage of maturity obtained
Where percentage of maturity obtained is <Current Age> / <Age at Maturity>. Round results down.
In 3e, we also get highly useful size modifiers. I'd suggest:
Infant: If current age is less than 1/4 age at maturity, reduce size class by two steps (tiny for humans).
Child: If current age is les than 2/3rds age of maturity, reduce size class by one step (small for humans). Also, the character gains the Lithe trait (see below).
LITHE [TRAIT]
Prerequisite: Dex 13, Size class small or smaller
Benefit: You may take your combat bonus due to size as a bonus to balance, climb, escape artist, jump, move silently, swim, or tumble skill checks provided that you are not encumbered and are wearing light or no armor. Additionally, the climb, jump, and swim skill checks depend on Dexterity rather than Strength.
Special: Creatures with the child template may utilize this trait even if they do not meet the normal Dexterity perquisite.
The bonuses for a size class imply the perceived increase in dexterity among children without erroneously making them more agile or giving them greater manual dexterity than adults.
From this I get very fine granularity. If I need for some reason to stat out a child who is 5 and another who is 10, I can produce very exacting differences between the two children so that it is easy to see how the 5 year old sees the 10 year old as big, strong, and knowledgeable.
As for level, generally most children are 0th level commoners. I still use 1e style minimum ability prerequisites, partially to maintain compatibility with my child rules (also to put a limit on multiclassing, and also provide explanation for why some characters never leave the commoner class). Once a child meets the minimum qualifications for a class, they can begin training in it, becoming initially a 0th level member of that class. If you pay for enough and sufficiently high quality tutoring, you can end up with a Charles XIII of Sweden or Paul Atreides or style dangerous child character.