In Matthew 28:18 – 20 Jesus said: “…All power is given unto me in heaven and in earth. Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you always, even unto the end of the world. Amen.” Since this Great Commission is given to all Christians, then it follows that the authority to baptize is also given to all Christians.

Based on this passage, it would seem that any true believer has authority from God to baptize, even as he has the authority from God to evangelize and teach all that Christ commanded.