Dostoevsky spends a great deal of time revealing the extremes of Kolya's character, because, at thirteen (nearly fourteen, as Kolya insists on pointing out), his soul is in the balance. Kolya is intelligent, and that means he's at great risk. Dostoevsky doesn't worry much about the fate of unintelligent people; they are bound to be either holy innocents or brutes. However, the smart can get themselves into serious trouble, and do serious damage, if their intellect outstrips or stifles their spiritual development.
Kolya is a convincing adolescent because he has embraced adult concerns (religion, politics) with all the enthusiasm of the new convert. But he is (pardon the anachronism; I just can't let it go) like a novice driver behind the wheel of a Ferrari. His mind is a powerful engine, which he doesn't have the faintest idea how to control, and so he's constantly crashing. He tricks a peasant into killing his own goose to prove a theory; he lies on railroad tracks and lets a train pass over him (fainting in the process, but developing a reputation as a "desperate character"); he finds and hides a stray dog--Ilusha's lost dog--for a month, in order to train the dog and surprise Ilusha. Kolya's training methods border on cruel, as does his notion that it's better to wait and surprise Ilusha, rather than just give him the dog back as soon as he finds him.* In all cases, Kolya's theories on the superiority of the intellect (especially his own) distort his good, or at least benign, intentions. But Kolya's goodness still comes through: he really does want to make Ilusha feel better, and he does, though at some cost to all concerned.
For this reason--the goodness showing through the cracks--Kolya attracts the attention of Alyosha, who functions as a true angel for the boy. Alyosha's at his most appealing in his interactions with Kolya, which shows us another benefit of creating complex children as characters: they allow your adults to show more interesting sides of themselves as well.
As Kolya recognizes, Alyosha treats him as an adult, which is what an intelligent child desires, and deserves, above all. And by this means, Alyosha gently makes Kolya aware of his errors:
“What do you think the doctor will say to him?” Kolya asked quickly. “What a repulsive mug, though, hasn't he? I can't endure medicine!”
“Ilusha is dying. I think that's certain,” answered Alyosha, mournfully.
“They are rogues! Medicine's a fraud! I am glad to have made your acquaintance, though, Karamazov. I wanted to know you for a long time. I am only sorry we meet in such sad circumstances.”
Kolya had a great inclination to say something even warmer and more demonstrative, but he felt ill at ease. Alyosha noticed this, smiled, and pressed his hand.
“I've long learned to respect you as a rare person,” Kolya muttered again, faltering and uncertain. “I have heard you are a mystic and have been in the monastery. I know you are a mystic, but ... that hasn't put me off. Contact with real life will cure you.... It's always so with characters like yours.”
“What do you mean by mystic? Cure me of what?” Alyosha was rather astonished.
“Oh, God and all the rest of it.”
“What, don't you believe in God?”
“Oh, I've nothing against God. Of course, God is only a hypothesis, but ... I admit that He is needed ... for the order of the universe and all that ... and that if there were no God He would have to be invented,” added Kolya, beginning to blush. He suddenly fancied that Alyosha might think he was trying to show off his knowledge and to prove that he was “grown up.” “I haven't the slightest desire to show off my knowledge to him,” Kolya thought indignantly. And all of a sudden he felt horribly annoyed.
“I must confess I can't endure entering on such discussions,” he said with a final air. “It's possible for one who doesn't believe in God to love mankind, don't you think so? Voltaire didn't believe in God and loved mankind?” (“I am at it again,” he thought to himself.)
“Voltaire believed in God, though not very much, I think, and I don't think he loved mankind very much either,” said Alyosha quietly, gently, and quite naturally, as though he were talking to some one of his own age, or even older. Kolya was particularly struck by Alyosha's apparent diffidence about his opinion of Voltaire. He seemed to be leaving the question for him, little Kolya, to settle.
“Have you read Voltaire?” Alyosha finished.
“No, not to say read.... But I've read Candide in the Russian translation ... in an absurd, grotesque, old translation ... (At it again! again!)”
Kolya's pomposity is obnoxious and funny at the same time; and his flustered self-awareness makes us care about him. With Alyosha's help, we forgive his blunders and feel genuine hope for his future.
So, in creating child characters, it might help to think of the child as a person at a crossroads. At stake is the kind of adult he or she will become. The child is trying on adult ideas and ways, playing dress-up, only the game is serious. The child lacks whatever adults possess that enables us to wear our grown-up costumes more successfully...which raises the question, what is that quality, exactly? Is that quality always desirable? In Kolya's case, through the conversation with Alyosha, we learn that empathy--which requires, according to Dostoevsky, belief in God--is the key to a meaningful life. Many adults don't have empathy, and Alyosha is determined to cultivate it in Kolya. Alyosha is like an author developing Kolya's character, acknowledging his cruel and awkward tendencies while drawing out his humanity. We, as authors, could try doing the same.
*I am still not a hundred percent certain that this dog is in fact Ilusha's lost dog. Because Ilusha's ill and also wracked with guilt--he thinks he killed his dog by tricking him into swallowing a pin (a stunt Smerdyakov, the villain, taught him)--Kolya may only be fooling him with a different dog. Either way, Kolya is doing a nice thing for Ilusha, but in an unintentionally mean way.