The presence of the nuclear family structure itself beyond a few centuries is quite disputed itself even. I personally don't agree with the assertion that nurseries are inherently modern. As far as I know, it was very common for neighbors to help each other out on a regular basis and help each other with various mundanities when the time called for it. It only seems to me that in the highly structured life of the dwarves, the need to instill a sense of community and an ethic of 'groupthink' would be very valuable, and nurseries certainly help that.
Of course, neighbours & extended family did take care of each other's children, as a personal favour. The difference with a nursery is that the children are given to a person to keep an eye on them and that person just does whatever he does otherwise, interrupting that work briefly as needed for wiping snot, tying shoelaces etc. In a nursery, children are brought to a specific place, with a professional paid caretaker who doesn't do other things than taking care of the children. The latter is too modern for my taste in the game; YMMV.
In practice, it's conceivable for female soldiers or smiths to drop off their child at a relative or at the meeting hall before hammering away. Weavers, cooks etc. would have their young children tag along, or in a backpack, possibly swaddled up, as Neonivek mentioned.