Their situation in al-Barzakh. It is proven that as soon as they die they are transferred to Paradise and that their souls are blessed there under the care of our father Ibraaheem (peace be upon him).
“We set off, and we came to a verdant garden, in which were all the colours of spring, where there was a man who was so tall that I could hardly see his head in the sky. Around the man was the largest number of children I had ever seen…” Then among things that the two angels explained to him was: “As for the tall man who was in the garden, that was Ibraaheem. As for the children who were around him, these are all the children who died in a state of fitrah.” One of the Muslims said: “O Messenger of Allaah, what about the children of the mushrikeen?” He said: “And the children of the mushrikeen.” Narrated by al-Bukhaari (7047).
And it was narrated that Ibn Mas’ood (may Allah be pleased with him) said:
The souls of the children of the believers are in the crops of birds which go wherever they want in Paradise and return to lamps hanging from the Throne. End quote.
Narrated by Ibn Abi Haatim with his isnaad. See Tafseer al-Qur’aan al-‘Azeem, 7/148
On the Day of Resurrection, people will be raised from their graves and the children will also be raised in the state of childhood and youth in which they died, and they will intercede for their parents and admit them to Paradise by Allah’s mercy towards them:
It was narrated that Abu Hassaan said: I said to Abu Hurayrah: Two of my sons have died. Can you narrate to me any hadeeth from the Messenger of Allaah (blessings and peace of Allah be upon him) which will console us for our loss? He said: Yes: “Their little ones are the little ones (da’aamees) of Paradise. When one of them meets his father – or his parents – he takes hold of his garment – or his hand – as I am taking told of the hem of your garment, and he does not let go until Allaah admits him and his father to Paradise.”
Narrated by Muslim, 2635
Ibn al-Atheer said: Da’aamees is the plural of da’moos.. refers to the one who wanders about, i.e., they go everywhere in Jannah, entering all places, and they will not be barred from any place, as children in this world are not barred from entering upon women and no one hides away from them. End quote. Al-Nihaayah, 2/279