Most of what we know about this is either incidental reporting or derives from contracts made with wetnurses that the wealthy could afford. So what peasant women throughout history fed their babies, isn’t all that easy to reconstruct, especially since circumstances were different depending on region, time, cultural ideas about childrearing and the socio-economic status of the mothers.

Throughout history, people seem to have mostly tried to tide their children over with milk, either human or animal, until they could eat solid foods ontheir own.

Antrophological data extracted from teeth shows that in prehistoric times, children weren't fully weaned until they were about between five to seven years of age. That fell drastically to about two years after humans started to settle, when babies and toddlers that didn’t have a full set of teeth yet, could be supplemented with milk from animals such as goats and sheep. They were also given pre-chewed regular food from adults.

From antiquity we know of nursing contracts that were valild until the baby reached the age of six months or the first tooth appeared. After that, the baby would be fed with, again, animal milk for another one and a half years. Women who weren't of the social class to afford a wetnurse would presumably breastfeed for longer than that.

During the middle ages noble children were fed by wetnurses until age two. Peasant women also seem to have breastfed for about two years as well and supplemented with mashed up foods or things like bread soup and porridges, until the child could chew its own food.

It’s important to note, that not everyone would have had access to animal milk for their baby. The availability of milk changed according to region and timeframe and season, so it was not always an alternative to breastfeeding or mashing up solid foods. Milk and dairy products could be a regular peasant food at one time in one place and a luxury only available to fairly rich people elsewhere at the same time. The laws for common grazing grounds changed in England at one point, for example, and had drastic consequences on whether peasants were able to keep a milk cow or not. That would naturally also influence the diet of small children.

Milk is also a seasonal product and only available after the animal has given birth some time in spring. In winter, you’d have to find something else to feed a baby, if you didn’t want to or could not breastfeed and the child was too young for solids.

Depending on such circumstances, the peasant woman in your example would most likely not have intentionally weaned her baby until it could chew solids on its own or at least eat some softer foods - if she had any of those available.