As an ordained minister of the Church of God (Anderson) I believe baptism by immersion was the normal practice of the early Church. The issues are complex; I am a credobaptist as well, not a paedobaptist. (Look those up if you care.)
However, what happens if baptism by immersion ("dunking" for the non-technical folks) is not feasible? What if a person is gravely ill? Should an immersionist like myself just shrug his shoulders and say, "Well, baptism doesn't save a person anyway so I won't do it"? I believe baptism is important; King Jesus demanded it of his followers. While there are times when immersion is impossible some occasions present themselves where a compromise can be reached.
There is an impressive ancient document from early Church history called the Didache, which is Greek for "teaching." While scholars debate the age they all arrive at an extremely early dating for the manuscript, from the mid-first century to the early second-century. In fact, even though consensus did not grow to include it as part of Bible canon (as one of the authorized books of the New Testament) some early Church Fathers did believe it was inspired Scripture. I don't think it is Scripture but its importance would be hard to be overstressed.
The Didache has a section on baptism. It reads as follows:
7 Now about baptism: this is how to baptize. Give public instruction on all these points, and then "baptize" in running water, "in the name of the Father and of the Son and of the Holy Spirit." 2If you do not have running water, baptize in some other. 3If you cannot in cold, then in warm. If you have neither, then pour water on the head three times "in the name of the Father, Son, and Holy Spirit." 4Before the baptism, moreover, the one who baptizes and the one being baptized must fast, and any others who can. And you must tell the one being baptized to fast for one or two days beforehand.
This certainly is interesting. It appears to me that this manuscript hints that the early Church baptized by immersion (or at the least they stood in a considerable amount of running [Greek: "living"] water). Notice, however, that the produced document isn't legalistic about the mode of baptism. It says, "Do A, but if you can't then do B, but if you can't then..."
If a person becomes a Christian in a hospital, on his sickbed, etc. and is in grave illness then I advise the immersionist minister to wrap a towel around the convert's neck and pour water on the new believer's head three times, "in the name of the Father, Son, and Holy Spirit."
Yes, the mode of baptism is important but it is not as important as the act of doing it, and the mode is far less problematic than a minister refusing to perform baptism if he can't do it in his theologically preferred way. It appears the early Church was flexible. I pray immersionists like me will be flexible as well.