Praise be to Allah.
This work is not permissible because it involves printing pictures of animate beings on shirts that children will wear, so the pictures will be openly displayed on the chest of the person wearing the clothes. The Messenger (peace and blessings of Allaah be upon him) said: “Allaah has cursed the makers of images” and “Every maker of images will be in the Fire.” It was reported that ‘Aa’ishah, the wife of the Prophet (peace and blessings of Allaah be upon him) told him that she had bought a saddle-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. [‘Aa’ishah said:] “I could see in his face that he was displeased and I said ‘O Messenger of Allaah, I repent to Allaah and His Messenger. What is my s in?’ The Messenger of Allaah (peace and blessings of Allaah be upon him) said: ‘What is this saddle-cushion for?’ I said, ‘I bought it for you so that you could sit on it and use it as a pillow.’ The Messenger of Allaah (peace and blessings of Allaah be upon him) said, ‘The makers of these images will be punished on the Day of Resurrection and it will be said to them, Bring to life that which you have created.’ And he said, ‘The angels do not enter a house in which there are images.’” (Narrated by al-Bukhaari, 5181)
This includes all images, whether they are carved, engraved, printed, drawn or taken with a camera, because all kinds of image-making are included in the general meaning of the hadeeth. There are no exceptions, apart from cases of necessity or need such as photos for personal identity documents, which are essential. But the case which you have mentioned in your question is not included in this exception. So look for another kind of work which is halaal. We ask Allaah to make what He has permitted sufficient for us so that we will not need to look to what is haraam, and to make us independent by His grace.
May Allaah bless our Prophet Muhammad and his family and companions, and grant them peace.