Man begets man, God begets God. Jesus is the only begotten son of God, and he is called God different times in the Bible, not just John 1:1.
I think son of God MEANS that he is God.
If you have a movie, say King Kong. And then a sequel, son of King Kong, the subject is going to be very similar, isn't it? Is there still only one King Kong, or are they both King Kongs, similar in power and image but different versions? One is not in essence less Kong than the other. (Please forgive the silly illustration! Um, cofty thinks God is a monster, so cofty, that was a gift to you! ;))
The Trinity doctrine is meant to reconcile how there can only be one God, yet there are all these scriptures that say the son of God is: the image of God, God, the alpha and Omega, the I am, the only begotten God, mighty God, all things created by him, etc.