Can only Christians administer baptism?

No. Anybody—even an atheist—can administer baptism if he has the proper intention. According to the Catechism of the Catholic Church (CCC 1256) “the intention required is to will to do what the Church does when she baptizes, and to apply the Trinitarian baptismal formula.” The reason anybody can baptize is that it is, in fact, Jesus Christ who performs the baptism. Once again, baptism is God’s grace to us, not our work for him.