If a baptism is done in the proper way like Catholics do, i.e. in the name of the Father, the Son, and the Holy Ghost and with water (symbolism) it is sufficient. Catholics, like the Apostles also partake of Holy Communion, (the highlight of our worship service) knowing that the bread and wine contains the "Real Presence" of Jesus Christ, that it is indeed His body and blood, just like He (Jesus) said and the Apostles believed, the same truth that they passed on to their successors. (see my quotes from the Early Church Fathers posted earlier).
The only thing you got right was the part about Baptists not believing in the "Real Presence". The other things you said came about only by your particular biblical interpretation.
Baptists believe in a "go it alone" idea that was far from those Apostolic days. There were no "Free and Independent" churches back then where everyone read the scriptures (which were not even compiled yet) and decided things for themselves.
There was hierarchy, a central authority, who told every Christian alive what to believe and how things should be seen. This is proved by such things as the letters to the Corinthians where they were told how they were getting things wrong and they had better get with the program.
So no, the early Christian Church in those days was assuredly not Baptist.