At the same time it feels rather unresponsible to bring the kid along to the DESERT OF DEATH where she sleeps half the time.
I can't deny that, but on the other hand, there's not much of a choice: nowhere to leave her in the meantime, and she wouldn't stay there anyway, if they tried to. It's also probably not strange from their point of view, although I wish the author depicted that by having more kids around. Now it's like Mu is the only one. In real history as well, the vast majority of children were put to work, to varying degrees, as soon as they had enough wits to be relied upon. Still today child labour is a problem in parts of the world (or at least a problem in the eyes of the older developed countries, the developing countries in question don't necessarily view it as a problem, just a part of their economy). In this series' case, it's also a factor that it's a world of magical skills that take a lot of effort and time develop. Mu is developing her skills all the time by going through all of this. Starting young, when she hits adulthood, she will possibly be a powerhouse already. Last but not least, as long as she doesn't die immediately, Touru can heal all wounds. So, the group's situation is kind of unique.