What is the status of Jesus within the Qur'an?
There are many verses speaking about Jesus the messenger of God.
His birth was the will of Allah:
[And mention] when the angels said, "O Mary, indeed Allah gives you good tidings of a word from Him, whose name will be the Messiah, Jesus, the son of Mary - distinguished in this world and the Hereafter and among those brought near [to Allah ] He will speak to the people in the cradle and in maturity and will be of the righteous. She said, "My Lord, how will I have a child when no man has touched me?" [The angel] said, "Such is Allah ; He creates what He wills. When He decrees a matter, He only says to it, 'Be,' and it is. And He will teach him writing and wisdom and the Torah and the Gospel. 3:45-47
Jesus was a messenger of Allah:
And [make him] a messenger to the Children of Israel, [who will say], 'Indeed I have come to you with a sign from your Lord in that I design for you from clay [that which is] like the form of a bird, then I breathe into it and it becomes a bird by permission of Allah . And I cure the blind and the leper, and I give life to the dead - by permission of Allah . And I inform you of what you eat and what you store in your houses. Indeed in that is a sign for you, if you are believers. And [I have come] confirming what was before me of the Torah and to make lawful for you some of what was forbidden to you. And I have come to you with a sign from your Lord, so fear Allah and obey me. Indeed, Allah is my Lord and your Lord, so worship Him. That is the straight path. 3:49
[Mention] when Allah said, "O Jesus, indeed I will take you and raise you to Myself and purify you from those who disbelieve and make those who follow you [in submission to Allah alone] superior to those who disbelieve until the Day of Resurrection. Then to Me is your return, and I will judge between you concerning that in which you used to differ. 3:55
Jesus was not killed:
And [for] their saying, "Indeed, we have killed the Messiah, Jesus, the son of Mary, the messenger of Allah ." And they did not kill him, nor did they crucify him; but [another] was made to resemble him to them. And indeed, those who differ over it are in doubt about it. They have no knowledge of it except the following of assumption. And they did not kill him, for certain. Rather, Allah raised him to Himself. And ever is Allah Exalted in Might and Wise. 4:157-158