Not a lot is known about the unnamed daycare center before the outbreak except that is had a playground and was designed specifically for small children and toddlers. The owners would look after and tend to children in the community while providing the children with nourishment and formula.
Once the outbreak started, the parents of the children got them from the daycare center and searched for aid at any evacuation center, most likely heading towards Atlanta.
After the events of "Killer Within", Hershel informs the group that the baby is healthy but requires formula in order to survive. Daryl and Maggie hop on the motorcycle to scavenge for supplies. They eventually found the abandoned Daycare Center and got the formula and some supplies for Judith then heads back to the prison.