What Catholics do and what Protestants do may appear similar, but they are considered to be very different things, by both parties. I think, and correct me if I'm wrong (like someone being wrong would ever get ignored around here anyway) that a Trinitarian Baptism is recognized between RCs and Paedobaptist Proddies. However...an RC baptized as an infant would not be recognized by the credo-Baptists. (And I am using the term Protestant in the strictist sense of the term, those who are Protesting, not the broad term applied to all non-RCs). Calvinists only see two sacraments: Baptism and Communion. We recognize RC Baptism, but our disagreement on the nature of Communion is enough for another thread.... I would say that Baptists would reject all infant baptism's.
We would have the adult believer be re-baptized by immersion as a symbol of his faith in the death, burial and resurrection of the Lord Jesus Christ.