Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
It is not a condition that circumcision be carried out by Muslim doctors. It can be done by anybody regardless of his religion, if no harm is feared from him.
However, it is more appropriate for the circumcision and all its treatment to be done by a Muslim doctor.
Allah knows best.