Ibn 'Abbas (may God be pleased with them both) narrated that the Prophet (peace and blessings be upon him) met some riders at Al-Rawha`. He asked them: 'Who are you?' They said, 'We are Muslims. Who are you?' The Prophet replied, 'I am the Messenger of God.' At this, a woman lifted a child and asked, 'Is hajj valid for this [child]?' The Prophet replied, 'Yes, and you will be rewarded' "[recorded by Muslim].

The ruling
Your son's hajj is valid provided you completed its integrals and duties on his behalf. As he will earn the reward of a voluntary hajj, it does not fulfill the obligation because obligatory acts of worship are only mandatory upon a legally accountable person, which a child is not.
And God the Almighty knows best.