Indeed Allah (SWT) is just. He is not an oppressor because the source of oppression derives from ignorance and lack of knowledge. Allah (SWT) is omniscient; He has all the capabilities and is thus far from any deficiency. The view Islam holds for this world is that of an ephemeral life, whereas it views the hereafter as the eternal life. In order to achieve an unlimited comfortable life in the hereafter, the righteous try to live a life free of sins and full of obedience to Allah (SWT). This may in many cases not be easy for them as they will face difficulties in this life; however they consider this world as a farm in which its products can be obtained in the hereafter. Consequently, children who die in their early ages will be departing this world in a sinless state, and therefore, will be showered with blessings in the hereafter. This concept has been discussed in the Islamic sources in more detail, for example it has been noted that after their death, Allah (SWT) will provide them a nanny and nurse to take care of them and help them to grow and reach perfection.
The death of children has many other divine underlying purposes. For example Allah (SWT) may want to test the faith of the child's parents. Their patience and strong faith can be a step toward their perfection. On the other hand, the child will also benefit from such a tragedy in that he/she will be showered with blessings in the hereafter.
Although we can not ever come to know the underlying reasons of all the acts of Allah (SWT), but our wisdom certifies that none of His acts are without purpose. Our lack of knowledge about something can never be proof for its non-existence.