Tough to builds a doctrine on the words that are not there huh?
The words are not in that small piece of Scripture you quoted, but are in other passages. At Pentecost, baptism is taught. In all 10 conversions in Acts, baptism is a central part. Paul himself was baptized to "wash away" his sins. If you look at the teaching of the entire New Testament, baptism is absolutely a part of the Gospel. A person who hears the Word, believes it, repents of their sins, confesses Jesus Christ as the Son of the living God, and is immersed for the remission of their sins has obeyed the Gospel.