Necro time! I was just thinking about how dwarven children could develop after reading a bit of a talk with Toady. My version is less complex than the OP.
Goal: by the time the dwarf has come of age, he has up to around Novice to Proficient level in one or two skills. I think that's fair.
The idea is that there would be two stages of childhood devolpment. In early childhood, they play. You can't control what they play at. In late childhood, they are apprenticed, and you can control that.
Playing should be a set of activities that a child dwarf chooses based on their aptitudes, inclinations, and what their parents do. Such activities could be:
- wrestling other children (for athletic children, children with warrior parents, children with belligerent personality traits): trains wrestling and other combat skills obviously
- building stacks of toys (creative children, those w/ craftsmen parents): trains masonry, or a crafting skill possibly and if, say, the toys are wood or metal it can train woodcrafting, carpentry, even metalcrafting – or mechanics (toy gears should be a thing)
- hunting and seizing vermin: trains hunting/animal training skill, also may make a child enjoy the outdoors
- gathering crops (like it is now, but less frequently/less skill gain): could also extend to foraging
- (rarely) playing with fire: trains furnace operator/ wood burner, but is obviously quite dangerous and you have to watch out for this!
Playing should get a young dwarf to dabbling most of the time, unless the dwarf's a genius. Also, trauma that is incurred during play might switch a dwarf's interests, like if he gets attacked while hunting for toads outdoors.
Late childhood, it's apprenticeship. By default, to one of his parents, or possibly an adult friend if the kid is "put off by authority and tradition," but you can assign the young dwarf, who now shows up as "apprentice", to any other dwarf you want. For the next couple of years, the child follows the master around and learns based on the same teacher/student/observer mechanics military dwarves learn by, so the more his master does in his chosen craft, the more the child learns. (And since it's patterned after the military mechanic, it's not that quick
)
Exception: children of the presiding nobles. These dwarves should be drains on your resources that you can't control! They should not be available as apprentices and get to do whatever they want, still. I can definitely see the son of the duke being an obnoxious dilettante who just decides to take one of the jobs you've asked your forge for and try forging a sword one day. Though it is far more likely they'd simply hang around chatting with other dwarves, or play at war if they're aggressive or athletic.
Loitering kids could be drawn to features like windows, trade depots, caged animals, and statues, instead of always hanging around the meeting areas.
So... then you would have adult dwarves with baseline proficiency in the skills your fort uses, depending on the skill of their teachers and how well they focused over their childhood.