Some play could even result in useful skills when the child matures. I know a few people who were inspired by childhood play (i.e. Lego blocks) to become architects or mechanical engineers.
Perhaps dwarven children could slowly gain forging skills while playing with a mini-forge, capped at novice level. Or instead of actually having the skills when they mature, the game could take advantage of the skill rusting system to treat play skills as "pre-rusted," so that the rate of real skill gain will be faster once maturity is reached. The same could be true for crafting and music skills once they're introduced.
That's a good idea. I think toy axes could train axe skill, toy crossbows (requiring toy bolts made out of, I donno, cloth probably) to train marksdwarf, archer, and (in absence of toy bolts) hammer skills, block sets to train masonry/carpentry/meatlworking (depending on material) and/or architecture...
I also suggest another stage of development: Toddler. Maybe babies would start to acquire child traits in the first third or so of the child stage, wandering away from their parent (causing the parent to come after if the toddler is far enough away or in danger), playing with other children/babies/idlers/parents/siblings/etc, giving random items as "gifts" to friends and family (I can personally confirm that toddlers do this), trying to pet tame (or not) animals but maybe accidently hurting them (also confirm, young children don't always have the self-control to not hurt animals they pet...although certainly not likely to punch the doggie in the head, jamming the skull through the brain, maybe dwarven chil.dren do), and of course getting into all kinds of trouble--falling down wells, getting lost in mines, trying to pet the big, furry tick with leathery wings and firey breath, giving a chunk of granite to a nice-looking green-skinned person with a big, sharp, fun-looking toy, etc--when not supervised.