To travel abroad, leaving the “Schengenraum”, Your child needs a child passport. Please ask the local civic office about the documents You need to apply for the passport. You have to know the rules of travel for the goal of Your journey as well as all the countries You are passing through. There may be different rules of travelling in all those countries.
You are advised to provide Your child with a Declaration of consent of the parents
to travel alone or with someone else if he or she does so. You should also state the starting point, the final destination and the reason for travelling. Declaration of consent of the parents you find here:
Einverständniserklärung für ein ohne Eltern reisendes Kind
Einverständniserklärung für ein mit nur einem Elternteil reisendes Kind