Simple: Dwarven children should cause trouble if they aren't happy.
When Dwarven children are upset but not enough so to start punching things at random, they should go around pulling levers and starting odd hauling jobs of their own initiative. They can't pass locked doors, so there are still ways to prevent total fortress melt down, but there should be a risk that kids occasionally cause that sort of thing so they're attended to. When temples are more clearly defined really rowdy children should be at risk for defiling one of them and being cursed somehow. There should be a risk of children lashing out at nobility in some non-lethal way or hiding/forbidding random supplies with no announcement, but also the chance of a mist zombie or wereskunk to suddenly be standing inside all of your defenses by a busted altar.
Aside from the regular mood changes from being near nice things, making some toys for the fortress should have slightly increased priority. Children should also benefit from good moods listening to songs and stories from their elders, possibly encouraging players to leave a couple of Dwarves idle as they'll naturally entertain children with their conversations and stories.
This creates some opportunities for Dwarven culture to become more central to the game. Once families are defined maybe children whose parents work in a different burrow get bad moods from not seeing them often. At the same time they benefit from contact with their family and with storytellers that are theoretically teaching them the kind of Dwarven values that make one question whether pulling the lever in the adamantine mine is really the right thing to do. If apprenticeship and other labors for children get implemented they could enjoy working with a parent at a workshop and learning the trade, or might dislike it based on their personality so they don't end up doubling the available hauling labor for the fort without any drawbacks.