Children Fasting (Hadith No. 1676)

Bismillah.
Volume 3, Book 31, Number 181:
Narrated Ar-Rubi' bint Mu'awadh (radiallaahu `anhaa):
"The Prophet (sallallaahu `alayhi wasallam) sent a messenger to the village of the Ansar in the morning of the day of 'Ashura' (10th of Muharram) to announce: 'Whoever has eaten something should not eat but complete the fast, and whoever is observing the fast should complete it.' "She further said, "Since then we used to fast on that day regularly and also make our boys fast. We used to make toys of wool for the boys and if anyone of them cried for, he was given those toys till it was the time of the breaking of the fast."

The Right Age

Fasting is not obligatory for young children, until they reach the age of adolescence, because the Prophet (peace and blessings of Allaah be upon him) said:
“The pens have been lifted from three: from one who has lost his mind until he comes back to his senses, from one who is sleeping until he wakes up, and from a child until he reaches the age of adolescence.”
Narrated by Abu Dawood, 4399; classed as saheeh by al-Albaani in Saheeh Abi Dawood
Nevertheless, children should be told to fast so that they can get used to it, and because the good deeds that they do will be recorded for them. 
The age at which parents should start to teach their children to fast is the age at which they are able to fast, which will vary according to each child’s physical makeup. Some scholars have defined this as being ten years of age.

Celebrate to Motivate

There is nothing wrong, in sha Allah, with the family celebrating the first time a boy or girl fasts, so long as it is limited to this occasion only, and will not become something that is repeated. There is nothing wrong with expressing happiness when the child reaches the age to observe this act of worship, or to encourage him and help him understand that this is an important event in his life. It is also a blessing for which thanks should be given to Allah. Some of the scholars regard it as mustahabb to make food for every happy occasion, and they specifically mentioned making food when a child completes the Qur’an.