Rex Wyler says, in The Jesus Sayings, page 73, that to the ancients, the dove depicted a new beginning. Thus, the representation is not so much of peace, but in each case, a new beginning:
The end of the Flood represents a new beginning, with Noah and his family repopulating the earth. The symbolism was so widespread that in the Epic of Gilgamesh, in the Flood of Utnapishtim, the dove also represents a new beginning.
The baptism of Jesus marks a new beginning. He begins to preach the gospel and fulfil the Old Testament.
James W. Kinn says (The Spirit of Jesus in Scripture and Prayer, page 40) that when the dove returned, Noah knew the flood was over, and in the next chapter God makes a covenant with Noah. So the dove is apparently a symbol of a new beginning. He says that in the Gospel, the dove was a new beginning for Jesus.
The connection between Genesis 8:11 and John 1:32 is the Promised Land. The dove was sent out three times looking for land. Jesus is the Branch of Jeremiah 33:15. Jesus is the Promised Land upon which the Spirit of the Dove descends and finds rest. The volume of the book is written of Jesus, Ps 40:7 and Hebrews 10:7. Note that it is the fourth time or "day" when you see the Dove come down on Jesus.
If I had laid the foundation for everything at once, you would have said I went off on a tangent. Sometimes less is more.
It is significant that three times Noah sent out the Dove and the fourth "time" you see the Dove is when it's spirit comes to rest on Jesus. It is the beginning of the fourth covenant generation after the flood. Scripture only uses the word "generation" or the word "day" for longer time periods and this is why I added these links to explain the "fourth day."
Jesus is the Word. Genesis 2:4 is only the example of the hyphenated compound word, creation-day. God created but told "man" to name it.
When Jesus tells you in Matt. 16:3 "ye can not discern the signs of the times" he is telling you that you do not know what time it is. He knows you can see the signs.
"Wise men know time and judgement," says the Preacher. Ecc. 8:5