Catholics-do you believe that if a baby dies who hasn't been baptised that they then go to hell?

This is NOT the teaching of the Catholic church and never was. Years ago, the Church taught that unbaptized babies went to limbo, not hell. In recent years, the teaching has changed. The Church teaches that unbaptized babies are taken back into heaven by an all merciful God. You have been given wrong information. You can get more information by going to Catholic.com and visiting the "Ask an apologist" section. There are many questions with official answers. You can even ask a question yourself.