Survival
This novel is written in such a way that we see a moment of Zlata's life before the war, when she was concerned with who's who at school, and who is popular, and what songs are on the radio. As a somewhat privileged child, she enjoys vacations and pleasant living condition. But then when war comes, everything changes. Instead of friends, the family's of the community are instantly tangled in a network of survival. Since most people were able to evacuate, the few remaining survivors learn the painful way that during wartime, because their very survival is at risk, any and all sacrifice that can be made must be made in order to survive—they burn their property to stay warm; they risk their lives just to get water.
Family cooperation
Because Zlata has both parents, and because both parents are willing and able to do whatever it takes to survive and to help Zlata, they avoid the worst fates, because it absolutely takes more than one person to survive. Zlata needs her father's sacrifices or else they won't survive, and when the father gets a hernia, the mother steps in and covers the gap. The value of the family is that it is a community where each person is willing to make sacrifices for the benefit of the group. At wartime, that means they are able to effectively cooperate.
The value of sacrifice
Ultimately, the primary virtue that this book teaches is love, but not an emotional love. Rather, the book demonstrates a committed kind of love that is willing to sacrifice one's own well-being for the betterment of a society or collective. In this case, that is typically the father risking his life to enter the war zone when necessary to obtain supplies and water. They also sacrifice their possessions to stay warm through the winter, and they sacrifice their privileged life style, making the most of their limited resources. These sacrifices are necessary, and it's because of their shared commitment to the family that they are willing to make them.