All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
You are not religiously obliged to take the responsibility of keeping this child with you, and you do not bear a sin if you refused this. Nevertheless, if you are able to take the responsibility and take care of him, it is more preferable, seeking the rewarded from Allaah The Almighty. It was narrated on the authority of Abu Hurayrah that the Prophet, sallallaahu ‘alayhi wa sallam, said: "Allaah Supports the slave (of Allaah) as long as he supports his (Muslim) brother." [Muslim]
However, if the child's parents are able to take him with them, they should do so, since having a child would not be an obstacle that prevents them from performing Hajj. But if they can not take him with them and further they do not find those who take care of him and they want to perform the obligatory Hajj, there are some details in this issue mentioned in Fatwa 92706, so refer to it.