The order is not given any importance. It is a spiritual circumcision, instead of just an outward symbol. The theme in verse 11 is circumcision, and in verse 12, it's baptism. Paul nicely connects them together. If circumcision is the mark of initiation of a person into the old covenant, baptism is definitely the mark of initiation into the new covenant.
Baptism is analogous to circumcision in the new covenant.
Baptism by itself does not have any effect. There must be belief involved. The baptism of an infant will only be useful if he professes his faith in Jesus once he is old enough. Correspondingly, Esau and Ishmael were circumcised, but it did them no good. Also, note that the thief on the cross was not baptized, but he went to be with Christ.