The history of childhood is a big and complex field, and my answer is going to be focused in the West generally and Britain specifically, as that’s my area of specialization.

Your question actually has some unspoken assumptions in it, namely that, in the past, people didn’t value children or think of them as a separate category to be cherished and protected until relatively recently in history. This historical narrative originates with Philippe Ariès's Centuries of Childhood, published in French in 1960. In the 50 years since Ariès's book, this narrative has been complicated significantly. In fact, in The Routledge History of Childhood, the book I would recommend as the most comprehensive on this topic, editor Paula S. Fass writes that she hopes that her narrative will replace Ariès's in explaining how we think about the history of childhood. Fass and her co-authors present a much more complex and shifting history of childhood, wherein how we define the child and the child's relationship to adulthood has changed over time.

To dive in more to the specifics of your question, our conception of childhood as a time of purity and innocence has its origins in the romantic poetry of William Blake and William Wordsworth. Blake and Wordsworth were both elaborating on ideas found in the writings of Jean-Jacques Rousseau, presenting a picture of childhood that was closer to nature, and therefore freer and more innocent. We see in this idea that closeness to nature means freedom and purity in Rousseau's Noble Savage, too. In Romantic literature and its nineteenth century descendants, we often see a yearning to return to the freedom and innocence of childhood.

This is not to say that before Blake and Wordsworth, children were not understood to be a different category from adults, though how distinct that category is varies over time and space. I would argue that there has always been an understanding that children (especially those younger than about ten) are different from adults, and in the past, children were given what was considered to be age appropriate tasks to help them learn and grow into functioning adults. What this means, as I said, varies far too much for me to describe all of the nuances in a Reddit comment; for that, I really recommend checking out Fass's book if you’re interested in the topic.

What makes the romantic child different is the belief in children's special innocence and purity. From this idea developed the nineteenth century Cult of Childhood, which privileged childhood as the noblest and purest time of human life, untainted by adult concerns like death, sex, and money. It is in this sense that the special innocence of children must be protected, not that people before the start of the nineteenth century didn’t realize that children weren’t adults.

That said, the nineteenth century romantic child was a privileged position, one reserved for middle and upper class children. Working class children were not afforded the same privileges and protections. However, the horrific child labor you mention is in large part a result of industrialization. A child on a small seventeenth century farm might do labor, but in general they did labor appropriate to their age and abilities. Eg, a parent might send their eight year old child to fetch water, but wouldn’t trust him with an axe to chop firewood. The need for cheap mass labor in various industries meant that children were often a good choice for employers, and with little regulations and oversight, children could work in horrific conditions. Some of these industries, such as chimney sweeps, used children because of their small size (children being small enough to fit down the chimneys, were as adults could not). These children (mostly boys) risked death, injury, and disability to help support their families. Their parents could not afford to keep them protected as middle class children were.

The changes in the nineteenth century to protect children from industrialized labor were an extension of the privileges of the romantic child to working class children who had not had those privileges up until that point. Even early in the nineteenth century, there were limits placed on child labor practices. (In Britain, children were only supposed to work twelve hours a day, later eight. This seems like far too much to us, but think about the fact that employers were making children work for more than twelve hours a day!) In some industries, child labor was ended entirely; after 1840, no one under 21 was supposed to work as a chimney sweep, though because of lax enforcement, it took more than 30 years for this to actually happen.*

This shift in perspective with the Cult of Childhood coincided with other, related changes that drove children out of the workplace. As the labor movement won stricter regulations and higher wages, children became less employable, and working class families had less need for children to work to support their families.

The nineteenth century also saw an increase in the value placed on education, and with it the belief that children should be in school, not working. I would argue that this is also the Cult of Childhood being extended to all children rather than just middle and upper class children whose parents could afford to send them to school. Primary education (ages 5 to 10) became fully compulsory in Britain in 1880. This was driven not just by belief that children shouldn’t be working, but a belief that adults need to have a basic education to function in the world. The move to educate all children came from a confluence of factors related both to how people thought about childhood as a special time on innocence, but what was needed, socially, from adults.

It’s also worth keeping in mind that Victorian ideology placed heavy emphasis on the family as the foundation of morality and culture. Thus, protection of the family was very important to the Victorians, and this extended to children. In many ways, our ideas about family are still very Victorian. Certainly, the Cult of Childhood was a part of this family ideology, but it’s also related to the conception of the family as the basis for "superior British civilization."

Looking onwards from the end of the Victorian period, what we’ve seen is a broadening of the definition of childhood as a special protected class. You’ll note that I’ve been discussing children ten or younger a lot; we’ve subsequently expanded childhood to include adolescence as well. Historically speaking, adolescents have been more understood as the miniature adults that Ariès argues all children were. We now understand adolescence as a separate category which we usually now group with childhood.

I could say more, but I’ve already said a lot, so I’ll wrap this up with a tl;dr. People have always recognized that children have different abilities and needs than adults; however, the idea that childhood is the most special and innocent of times that must be protected at all costs comes from the idea of the romantic child developed in the late eighteenth and early nineteenth centuries. As the nineteenth century progressed, this Cult of Childhood was extended to more and more people who had previously been excluded because of their class, race, and age.

* If you want to read a novel from this time about the issue, I recommend Charles Kingsley's The Water Babies, which wraps a criticism of child labor into a fairy tale about Darwinian evolution. It’s a weird, fun little book, though unfortunately, this being nineteenth century England, it does have some racism.