I've seen the claim made that it was in Victorian England, that children's books, children's toys, and children's entertainment exploded as a result of dropping infant mortality, urbanization, and more disposable income, which is why I wrote it in there, but exactly when and how and to what degree is widely debated. I'll try to give you the quick version so we don't move too far off from Victorian princesses! The conversation in academia starts with French scholar Philippe Ariès in 1960 with Centuries of Childhood. Today's scholarship about historical childhood goes back to Ariès. In that book, he argues that for a long time children were seen as tiny adults, and his main evidence is that in artwork children are depicted that way. He points to the whole idea of childhood originating around the 15th century, and even after that children were distinguished chiefly as being capable of different tasks for the family. Remembering that life was mainly rural and agrarian, you can understand why this might be (particularly if, like me, you grew up on a farm). In the Middle Ages, he writes, there also wasn't an effort to keep children in sexual ignorance as there was later: peasant children would sleep in the same bed as their parents, for example. Another important point is that child mortality was very high. If a child survived to around ten, they might be expected to live to adulthood, but especially the first few years of life were doubtful.

In The History of Childhood (1999), a collection of essay, it's shown that by the 17th-18th century in Europe, childhood was increasingly seen as precious. Ideas of childhood innocence and sanctity rose. There was a new idea that children could be morally corrupted by sexual knowledge, and complete ignorance was ideal. Child mortality remained high, but now parents, to put it bluntly, might expect their children, in general, to live. And yes, especially, children being kept out of work and given a time to play, explore, and "be children" in the modern sense is given increasing value. It was now seen as essential and regenerating for children. The author of the 19th century chapter, Priscilla Robertson, compares the middle class family to a nest (using a contemporary analogy). The role of the governess in both education (moral as well as academic) was paramount, and the idea of giving children outings and means to explore their imagination (and "imaginativity") expanded.

In A History of Childhood: Children and Childhood in the West from Medieval to Modern Times (2001), Colin Heywood describes these trends, including the idea that, even while childhood was being seen as more sacred and to be cherished around this time, the expansion of education also meant that children were increasingly formally educated and trained from a fairly early age for professions. It should absolutely also not be forgotten (and I admit I didn't stress this) that my description is largely for the middle class and up. Children from poorer families, especially in the city, would have been too busy playing the rather less amusing "six day work week" and "try-not-to-get-mangled-by-machinery-while-working-fourteen-hours-a-day" to have the kind of indulged childhood I described. Also, despite the introduction of universal education with the Elementary Education Act of 1870, children for much of the Victorian period remained illiterate, so sweet children's books would have been out of their reach, as would the theater, though public puppet theaters would certainly have been a way of picking up fairy tales, as would stories told by family and friends.

The most exhaustive book I've come across on children's lives in the Victorian era is Thomas Edward Jordan's Victorian Childhood from 1987. It's by no means the last word on the subject, but I suggest it for its very thorough and statistical attempt to describe childhood across the social spectrum, including lots about schooling, labor, and a whole chapter on children's outings! There's also plenty about children's crime (think Oliver Twist).

Of course, Ariès's argument should be taken with a grain of salt. Children of all times in history have played, and we have descriptions of it surviving. Even your soot-faced London urchin would have a little time to play and maybe to imagine a better life in between being stuffed up chimneys or into huge machines. Also, archaeologists have found children's toys going back thousands of years (I've had the pleasure of seeing firsthand toys from ancient Egypt), and even cultures that did not make toys likely to survive almost surely made toys from other materials (rags, sticks, corn husks, etc.) for children to play with. The claims of some of the historians of childhood that this was so children could practice adult skills (child-rearing, fighting, etc.) shouldn't be overlooked, but I think we can also agree that there is an element of fun to swordfighting or playing with a doll that is quintessentially the realm of children.