Praise be to Allah.
The basic principle is that it is forbidden to draw and make images of animate beings, whether that is by carving (statues) or on paper, fabric or anything else, and whether the image is realistic or imaginary, because of the stern warning concerning that which is narrated in the religious texts, such as the words of the Prophet (blessings and peace of Allah be upon him): “The people who will be most severely punished on the Day of Resurrection will be the image-makers” Narrated by al-Bukhari (5950) and Muslim (2109).
But an exception is made from that for images and three dimensional objects (toys) with which children play, because of the hadith of ‘A’ishah (may Allah be pleased with her), who said: The Messenger of Allah (blessings and peace of Allah be upon him) came back from the campaign to Tabuk or Khaybar and there was a curtain over her niche. The wind lifted the edge of the curtain and uncovered ‘A’ishah’s toy dolls. He said: “What is this, O ‘A’ishah?” She said: My dolls. He saw among them a horse with two wings made of cloth and he said: “What is this that I see in the midst of them?” She said: A horse. He said: “What is this that I see on it?” She said: Two wings. He said: “A horse with wings?” She said: Have you not heard that Sulayman had horses with wings? She said: And the Messenger of Allah (blessings and peace of Allah be upon him) smiled so broadly that I saw his eyeteeth. Narrated by Abu Dawud (4932); classed as sahih by al-‘Iraqi in Takhrij al-Ihya’ (2/344) and by al-Albani in Sahih Abi Dawud.
Al-Hafiz Ibn Hajar said in Fath al-Bari (10/527): This hadith is quoted as evidence that it is permissible to keep dolls and toys for girls to play with. This is an exception from the general prohibition on keeping images. This was stated definitively by ‘Iyad, who narrated it from the majority of scholars, and said that they permitted the sale of dolls to girls for the purpose of training them from a young age to take care of their houses and their children. End quote.
This indicates that it is permissible for children to make these three-dimensional objects themselves, or for them to be made for children.
Based on that, there is nothing wrong with producing cartoons for children, if they are free of haram things such as music, because of the proven concession regarding images for children, and because making such films in accordance with Islamic guidelines helps to reduce evil and occupies children with that which is beneficial or permissible.
There is nothing wrong with making a lion-type baby character, and giving it eyes and a nose.
Dr. Ahmad al-Qadi (may Allah preserve him) said: I asked our shaykh [i.e., Ibn ‘Uthaymin, may Allah have mercy on him]: What is the ruling on educational cartoons for children, such as the movie Muhammad al-Fatih?
He replied: There is nothing wrong with that, because it is beneficial, and because it will distract them from things that would harm them…"(Thamarat at-Tadwin min Fatawa Ibn ‘Uthaymin).
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) was asked: I hope that you can explain to me the ruling on buying videos if there are cartoons in them, noting that these cartoons are for a good purpose and benefit children. And is the ruling different if the images are static (not moving) or animated (moving), or not?
He replied: With regard to these movies which contain beneficial material, and benefit children and keep them away from things that are worse than them, if there is no other alternative, then undoubtedly they are less serious than indecent movies, and concessions are granted for children with regard to leisure and play that are not granted to adults. Hence the Prophet (blessings and peace of Allah be upon him and his family) granted a concession to ‘A’ishah (may Allah be pleased with her) allowing her to play with dolls, because he married her when she was young. When he married her she was six years old, and he consummated the marriage with her when she was nine years old, and he (blessings and peace of Allah be upon him) was the best of people to his family. He would allow her to play with these toys. Thus a concession is granted to children that is not granted to adults. So if a person buys movies which entertain children and do not contain any haram elements, there is nothing wrong with that.(Al-Liqa’ ash-Shahri, no. 47).
He (may Allah have mercy on him) was also asked: Many toys contain images of animate beings drawn by hand, and the purpose behind them is usually to educate the child, such as those that are found in talking books. Is that permissible?
He replied: If that is for the purpose of entertaining children, then the scholars who permitted toys for children also permitted such images, on the grounds that these images are not exactly like the images in which Allah created the creatures that are depicted, as is clear from what I see before me, so the matter is not that serious."(Majmu‘ Fatawa wa Rasa’il al-‘Uthaymin 12/339).
It is permissible to make a cartoon series on the internet and to design an animated character to answer questions, if that is specifically for children, because of the concession allowing that, as noted above. And there is nothing wrong with receiving payment for that, because whatever is permissible to make or produce, it is permissible to sell it or rent it out.
To sum up:
It is permissible to make a cartoon video series for children, if it is for a good purpose and is free of haram things such as music or spreading deviant ideas and beliefs.
And Allah knows best.