I wasn't qualified to answer the OP, although I feel almost pleased that the following answers are rooted in common sense and a logical progression.
thanks.
61.*And (Jesus) shall be a Sign (for the coming of) the Hour (of Judgment): therefore have no doubt about the (Hour), but follow ye Me: this is a Straight Way.
62.*Let not the Evil One hinder you: for he is to you an enemy avowed.
63.*When Jesus came with Clear Signs, he said: "Now have I come to you with Wisdom, and in order to make clear to you some of the (points) on which ye dispute: therefore fear Allah and obey me.
64.*"For Allah, He is my Lord and your Lord: so worship ye Him: this is a Straight Way."
65.*But sects from among themselves fell into disagreement: then woe to the wrong-doers, from the Penalty of a Grievous Day!
66.*Do they only wait for the Hour - that it should come on them all of a sudden, while they perceive not?
67.*Friends on that day will be foes, one to another,- except the Righteous.
Quran 43:61-67
Here's an example of the reaction from what remains of the previous scripture and the narrations recorded therein
23When Jesus returned to the temple courts and began to teach, the chief priests and elders of the people came to Him.
“By what authority are You doing these things?” they asked.
“And who gave You this authority?”
24“I will also ask you one question,”Jesus replied,*“and if you answer Me, I will tell you by what authority I am doing these things.*
25What was the source of John’s baptism? Was it from heaven or from men?”
They deliberated among themselves and said, “If we say, ‘From heaven,’ He will ask, ‘Why then did you not believe him?’26But if we say, ‘From men,’ we are afraid of the crowd, for they all regard John as a prophet.”*
27So they said to Jesus, “We do not know.”
“Neither will I tell you by what authority I am doing these things,”He replied.
From matthew 21
Allah's testimony is the best testimony:
12."O Yahya! take hold of the Book with might": and We gave him Wisdom even as a youth,
13.*And piety (for all creatures) as from Us, and purity: He was devout,
14.*And kind to his parents, and he was not overbearing or rebellious.
15.*So Peace on him the day he was born, the day that he dies, and the day that he will be raised up to life (again)!
Quran 19:12-15
5.*Has not the story reached you, of those who rejected Faith aforetime? So they tasted the evil result of their conduct; and they had a grievous Penalty.
6.*That was because there came to them Messengers with Clear Signs, but they said: "Shall (mere) human beings direct us?" So they rejected (the Message) and turned away. But Allah can do without (them): and Allah is free of all needs, worthy of all praise.
Quran 64:5-6
...Google says Mary and Joseph were Jewish.. do they do the whole circumcision thing? o_0
What remains of the previous scripture and narrations within it state the following:
16So they hurried off and found Mary and Joseph, and the baby, who was lying in the manger.17When they had seen him, they spread the word concerning what had been told them about this child,*18and all who heard it were amazed at what the shepherds said to them.*19But Mary treasured up all these things and pondered them in her heart.*20The shepherds returned, glorifying and praising God for all the things they had heard and seen, which were just as they had been told.
21On the eighth day, when it was time to circumcise the child, he was named Jesus, the name the angel had given him before he was conceived.
Jesus Presented in the Temple
22When the time came for the purification rites required by the Law of Moses, Joseph and Mary took him to Jerusalem to present him to the Lord*23(as it is written in the Law of the Lord, “Every firstborn male is to be consecrated to the Lord”b*),*24and to offer a sacrifice in keeping with what is said in the Law of the Lord: “a pair of doves or two young pigeons.”
c25Now there was a man in Jerusalem called Simeon, who was righteous and devout. He was waiting for the consolation of Israel, and the Holy Spirit was on him.*26It had been revealed to him by the Holy Spirit that he would not die before he had seen the Lord’s Messiah.*27Moved by the Spirit, he went into the temple courts. When the parents brought in the child Jesus to do for him what the custom of the Law required,*28Simeon took him in his arms and praised God, saying:29“Sovereign Lord, as you have promised,you may now dismiss your servant in peace.30For my eyes have seen your salvation,31which you have prepared in the sight of all nations:32a light ftion to the Gentiles,and the glory of your people Israel.”33The child’s father and mother marveled at what was said about him.*34Then Simeon blessed them and said to Mary, his mother:
“This child is destined to cause the falling and rising of many in Israel, and to be a sign that will be spoken against,*35 so that the thoughts of many hearts will be revealed. And a sword will pierce your own soul too.”
From Luke 2
The post birth rituals described are in keeping with the ways of Islam (the final and completed guidance) although a sheep or cow etc is usually sacrificed for the akikah by those who can afford it.