Is it permissible for children to draw pictures of animate beings?

Firstly: 

It is not permissible to draw and make images of animate beings, whether they are engraved, on paper, on cloth or anything else, because of the report narrated by al-Bukhaari (2105) and Muslim (2107) from ‘Aa’ishah the Mother of the Believers (may Allaah be pleased with her), that she bought a cushion on which there were images. When the Messenger of Allaah (peace and blessings of Allaah be upon him) saw it, he stood at the door and did not enter. She said: I recognized displeasure in his face. I said: O Messenger of Allaah, I repent to Allaah and His Messenger, what have I done wrong? The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “What is this pillow?” She said: I bought it for you to sit on and recline on. The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “The makers of these images will be punished and it will be said to them, ‘Bring to life that which you have created.’” Then he said: “The house in which there are images is not entered by the angels.”  

And Muslim (2110) narrated that Sa’eed ibn Abi’l-Hasan said: A man came to Ibn ‘Abbaas and said: I am a man who makes these images; advise me about that. He said to him: Come close to me. So he came closer to him. He said: Come closer to me. So he came closer to him, until he put his hand on his head and said: I will tell you what I heard from the Messenger of Allaah (peace and blessings of Allaah be upon him). I heard the Messenger of Allaah (peace and blessings of Allaah be upon him) say: “Every image maker will be in Hell, and for every image that he made, a soul will be created which will punish him in Hell.” He said: If you must do that, then make (images of) trees and inanimate things. 

Al-Nawawi (may Allaah have mercy on him) said in Sharh Saheeh Muslim: Our companions and other scholars said: Making images of animals is emphatically haraam and is a major sin, because this stern warning which is mentioned in the ahaadeeth is issued concerning it. That applies whether he makes it to be used in ways that are not respectful or otherwise. Making it is haraam in all cases, because it is competing with the creation of Allaah. That applies whether the image is in a garment or a carpet or a dirham or a dinar or a penny or a vessel or a wall or anything else. As for making images of trees, camel saddles and other things in which there are no images of animals, that is not haraam. End quote. 

It says in Fataawa al-Lajnah al-Daa’imah (1/479): What makes images forbidden is the fact that they are images of animate beings, whether they are sculptures, or drawings on walls or fabric or paper, or they are woven, and whether they are done with a quill, a pen, or a machine, and whether they represent something real or something imaginary, whether they are small or large, beautified or distorted, or drawn in the form of lines representing a skeleton. What makes them forbidden is that fact that they depict animate beings, even if they are imaginary like pictures of ancient people, Pharaohs, or leaders and soldiers of the Crusades, or like the pictures of ‘Eesa (Jesus) and Maryam (Mary) that are kept in churches, etc., because of the general  meaning of the texts, and because that is competing with the creation of Allaah, and because it is a means that leads to shirk. End quote.  

Secondly: 

Even if the child is not yet accountable, his guardian should prevent him from doing haraam things and discourage him from doing them, so as denounce evil and to train the child and make him get used to what is good. 

Allaah says (interpretation of the meaning): 

“O you who believe! Ward off yourselves and your families against a Fire (Hell) whose fuel is men and stones, over which are (appointed) angels stern (and) severe, who disobey not, (from executing) the Commands they receive from Allaah, but do that which they are commanded”

[al-Tahreem 66:6]

And the Prophet (peace and blessings of Allaah be upon him) said: “Each of you is a shepherd and each of you is responsible for his flock. The ruler of the people is a shepherd and is responsible for his flock. A man is the shepherd of his household and is responsible for his flock. A woman is the shepherd of her husband’s house and children and is responsible for her flock.”

Narrated by al-Bukhaari (893) and Muslim (1829). 

The child’s guardian should raise him to keep away from making images and drawing animate beings, and he should explain to him that this is haraam. 

He should look for permissible alternatives that are available, praise be to Allaah, such as drawing vegetables, fruits, trees and oceans, and any inanimate objects. 

And Allaah knows best.