May the priest baptize an infant at the Sunday celebration of the Eucharist?

Yes. The Rite of Baptism for Children, Introduction, Part III #9 states:

To bring out the paschal character of baptism, it is recommended that the sacrament be celebrated during the Easter Vigil or on Sunday, when the Church commemorates the Lord’s resurrection. On Sunday, baptism may be celebrated even during Mass, so that the entire community may be present and the relationship between baptism and eucharist may be clearly seen; but this should not be done too often.

Further clarifications were sent by the Congregation for Divine Worship in 1973 that state:

As often as baptism takes place during Sunday Mass, the Mass for that Sunday or on Sundays in the Christmas season and in ordinary time the Mass for the baptism of children is used. This can be found on p. 973 of the Roman Missal, third typical edition.