Another idea which tends to be thrown around is that the dove is symbolic of the Holy Spirit. Why? Because all four gospels describe Jesus' baptism using dove-terminology:
...he saw the Spirit of God descending as a dove and lighting on Him (Matthew 3:16)
...He saw the heavens opening, and the Spirit like a dove descending upon Him (Mark 1:10)
...the Holy Spirit descended upon Him in bodily form like a dove (Luke 3:22)
...the Spirit descending as a dove out of heaven (John 1:32)
None of these passages state that the Holy Spirit possessed the physical body of a dove. Note the type of language being used in these passages: they state that the Holy Spirit descended like a dove. The problem with linking this event to Noah's dove (other than the lack of any clear evidence of such a connection) is this: Why not link Noah's dove to one of the other passages in Scripture which mention doves?
For instance, Hosea 7:11 states that Ephraim has become like a silly dove, without sense. Solomon states that his love's eyes are like doves (Song of Solomon 4:1). Hezekiah states: I moan like a dove (Isaiah 38:14). Jesus said to be shrewd as serpents and innocent as doves (Matthew 10:16).
Does it really make sense to put together all of these dove references and come up with some sort of contradictory "doveology" symbolism to apply to Noah's dove? Even if a consistent symbol can be found in Noah's dove, one thing is known for sure: Noah did not send out the dove because of what it might have become a symbol of in the future. In fact, dove symbolism was probably the last thing on Noah's mind as he managed an ark filled with every kind of animal on the face of the earth.
Perhaps one day, in heaven, someone will finally be able to ask Noah, "Why did you send out the dove?" And maybe... just maybe, Noah will respond, "The only bird I disliked more than the dove was the raven."
A New Year, A New Era, A New World - Genesis 8:13
Noah Sends Out An Unsymbolical Raven (Part 1) - Genesis 8:6-7
The Chronology of the Flood: The Raven and Dove - Genesis 8:6-12
The First Sight Of The Post-Flood World - Genesis 8:5
Noah's Obedience - Genesis 6:22