Can small children actually commit morally wrong acts?
It depends on the age and ability of the child, but in general the answer is unfortunately, "yes." There are cases mentioned in the paper of children as young as eight or ten committing murder with guns. "They cited the example of Nathaniel Abrahams, a young black boy who has experienced many disappointments from his parents. Nathaniel rebelled and began to commit crimes at the age of eleven. He killed, robbed and flashed guns to intimidate. He was later arrested and charged with adult crime." ["Why Juveniles Commit Crimes" by Joseph A. Wickliffe]. Not long ago I talked with a distraught mother whose four-year-old was sexually molested by the five-year-old child of a friend. It was shocking and nauseating, but very sadly all too true. As every parent can attest, a small child will on occasion tell lies. See the questions and answers section at the end of "Five to Nine Year Olds: Responsibility Training" to see that it does happen.
The question should not be "can a child commit a morally wrong act" because the evidence is plain that they do; instead, the question should be "does a child, who commits a morally wrong act, know what he is doing?" For very young children, the answer is "no." Oh, a child who tells a lie at age five knows that he didn't tell the truth, but he doesn't know the concept of right and wrong. He might see it as a way to manipulate others, to avoid punishment, or to gain something he wants. It is much like a child who becomes frighten by a television show. He can tell you that it is a TV show, but he isn't able to truly distinguish between make-believe and reality. Thus he can tell you it is a make-believe story, but it is still scary because it might happen to him.
In the Bible this is referred to as possessing the knowledge of good and evil. God punished the Israelites for rebelling against Him by having them wander in the wilderness for forty years until that generation died off. However, He stated, "Moreover your little ones and your children, who you say will be victims, who today have no knowledge of good and evil, they shall go in there; to them I will give it, and they shall possess it" (Deuteronomy 1:39). The children might have imitated their parents in saying rebellious words, but God did not hold them accountable because they were too young to know better.
Exactly when a child gains the ability to make moral judgments is hard to say. See some of the past answers on the topic of "Age of Accountability" for a detailed discussion. Until a child reaches the age to make moral decisions on his own, it is up to his parents to guide him in making the appropriate decisions -- giving him encouragement in making good choices and punishing bad choices.