Qur'an 24:2—(As for) the fornicatress and the fornicator, flog each of them, (giving) a hundred stripes, and let not pity for them detain you in the matter of obedience to Allah, if you believe in Allah and the last day, and let a party of believers witness their chastisement.
Yes, it is similar to the laws given to us through Moses
“‘If a man commits adultery with another man’s wife—with the wife of his neighbor—both the adulterer and the adulteress are to be put to death. - Leviticus 20:10
I think it's important to point something out about both texts. Even if you disagree that extra-marital sex should be punished this severely you must also recognize that both participants - men and women should bear responsibility. Not just the woman. There is a lot of information missing in Hena Begum's case. Was she raped? From what I can tell about the part of the world, it wold not have mattered if she was raped or wanted it. Another source says she was raped by her cousin who is 40 years old. Was her cousin also given the same penalty of 100 lashes? I don't think that she deserved what happened to her. Nor do I think that she deserved to die even if she chose to be in the act freely. The thing I want to call attention to is that adultery and fornication are wrong because of how it damages the people who engage in it. God prohibited sex outside of marriage because it is better for us not because he doesn't want us to enjoy sex. It was illegal according to both the Qur'an and the Books of Moses to punish adultery only by punishing the woman. This is why Jesus did not condemn the woman who was brought to him who was caught in adultery. The religious leaders who brought her was only interested in trapping Jesus into either breaking the Law or stoning her. He turned the tables and although he didn't condemn her, Jesus told her to sin no more. This is what Jesus came for and we are all like that woman. We deserve to be stoned and to die in our sins, but Jesus came that we can live - not that we can keep sinning.
2 At dawn he appeared again in the temple courts, where all the people gathered around him, and he sat down to teach them. 3 The teachers of the law and the Pharisees brought in a woman caught in adultery. They made her stand before the group 4 and said to Jesus, “Teacher, this woman was caught in the act of adultery. 5 In the Law Moses commanded us to stone such women. Now what do you say?” 6 They were using this question as a trap, in order to have a basis for accusing him.
But Jesus bent down and started to write on the ground with his finger. 7 When they kept on questioning him, he straightened up and said to them, “Let any one of you who is without sin be the first to throw a stone at her.” 8 Again he stooped down and wrote on the ground.
9 At this, those who heard began to go away one at a time, the older ones first, until only Jesus was left, with the woman still standing there. 10 Jesus straightened up and asked her, “Woman, where are they? Has no one condemned you?”
11 “No one, sir,” she said.
“Then neither do I condemn you,” Jesus declared. “Go now and leave your life of sin.” - John 8:2-11
I think this is the best was of dealing with such situations. Love the sinner and shun the sin - not ignoring it.
Answering Muslims: Fifteen-Year-Old Hena Begum Dies after Receiving 100 Lashes
Bangladeshi teen dies from sharia lashing after reportedly being raped