I think all of that is contained in the concept of a "personal conversion experience"...
I was 9 years old when I "got saved" and was baptized. I was never a profligate sinner, but always raised in church in a godly and loving family. Truthfully, I believe I was "saved" -- I had faith in Christ and knew Him as my Lord and friend -- from the time I was a very small child. I do think turning to Him publicly was important, and the more I read, the more value I place on my baptism -- but no, I don't think either praying a prayer or doing a thing is in itself essential. It's faith, and the faith of a child is more than enough.
But I do believe Jesus commands us to do things, like baptism, and that they are more than symbols or empty acts of obedience. But that doesn't mean that He can't give us the same gifts by grace through faith.