The life of Jesus is recorded separately in four different books of the Bible. These four books are collectively called The Gospels. Some of them record details of Jesus early life and some do not:
- Matthew - Records His birth and then a visit from the wise men before fleeing from Herod to Egypt. The book then skips to His baptism as an adult.
- Mark - Contains no information about His childhood.
- Luke - Records His birth and circumcision. The book then skips to an incident when He was twelve years old and visited the temple. It then jumps to his baptism as an adult.
- John - Contains no information about His childhood.
The closest thing that the Bible comes to describing the rest of Jesus' early life is the following verse:
Luke 2:40 (NASB)
The Child continued to grow and become strong, increasing in wisdom; and the grace of God was upon Him.
As you can see, none of the Gospels describe the incident that you quoted from the Quran, nor any of the circumstances surrounding it. I am unaware of any mainstream Christians who would consider that story in the Quran to be an accurate account.
Although the Bible doesn't address Jesus' childhood in detail, it does describe a time when Jesus, during His public ministry as an adult, visited His home town of Nazareth. The events that happened there may indirectly shed some light on His childhood:
Matthew 13:53-58 (NASB)
When Jesus had finished these parables, He departed from there. He came to His hometown and began teaching them in their synagogue, so that they were astonished, and said, “Where did this man get this wisdom and these miraculous powers? Is not this the carpenter’s son? Is not His mother called Mary, and His brothers, James and Joseph and Simon and Judas? And His sisters, are they not all with us? Where then did this man get all these things?” And they took offense at Him. But Jesus said to them, “A prophet is not without honor except in his hometown and in his own household.” And He did not do many miracles there because of their unbelief.
Also, see Mark 6:1-6 for a parallel account. Although that passage does not specifically say so, it does seem to imply that Jesus did not regularly perform miracles during his childhood.