This is a follow up to an earlier question about a post apocalyptic ‘civilization’ created only from those under sixteen, and not many of them. Thus, anyone who can work is needed. What tasks might be assigned to children from 3/4-7/8 or so? They need tasks associated with making clothing, food (both farming animals and crops, and cooking), building, items such as dishes and candles for use and trade, and have to take care of even younger babies and toddlers.
Children of that age range are tremendous imitators, and while their motor skills and strength might not be up to par with that of older children, they should be able to complete relatively simple tasks of a repetitive nature, though, as @RonJohn mentioned in the comments, there would almost certainly have to be some level of supervision from older children to ensure they stayed on track. A few tasks come to mind:
(These specific suggestions are assuming your group is in a sort of woodland type area, with a fair variety of plants.)
- Cracking nuts for food supplies - Tedious, and not well-suited to those with greater specialization, but not that difficult. a rock to bang on, and a basket or container of some sort should suffice.
- Continuing in the vein of collecting food, picking berries is a great job for younger kids, provided they can be persuaded not to eat them all.
- Tending crops, if the survivors have managed to grow any, including, but not limited to, tasks such as: planting seeds, watering crops, and harvesting any grown crops. (Weeding might require more concentration than would be common to children this age.)
- Carrying firewood, and collecting brush. This is a simple chore that kids have been doing in many cultures for ages, and requires no great size or strength, but is still very necessary.
- The more nurturing children could play with any toddlers and babies in the group, and make sure they stay within a safe area.
- If the survivors are trying to craft items such as rope, younger children would be good for tasks in the vein of twisting together strands of bark, or other materials.
It's also worth noting that young kids, with their curiosity and ability to notice little things, make great collectors of things like nuts, or any item that became of value to the survivors.