To understand the "divorce" provision offered by Jesus, you must look at the context:
Matthew 19:7-9 They *said to Him, "Why then did Moses command to GIVE HER A CERTIFICATE OF DIVORCE AND SEND her AWAY?" He *said to them, "Because of your hardness of heart Moses permitted you to divorce your wives; but from the beginning it has not been this way. "And I say to you, whoever divorces his wife, except for immorality (porneia), and marries another woman commits adultery."
They are clearly discussing the Law of Moses by the context of saying "why then did Moses command" and "Moses permitted", and by the fact that tyhe Pharisees speak of the "CERTIFICATE OF DIVORCE" which only appears in Deuteronomy 24:1. Therefore the allowance must be for porneia which means fornication, and must be found when the man married her. The man couldn't find fornication in his wife at a later date, because by then she would be expected to not be a virgin since presumably he would have consummated the marriage. The passage makes perfect sense once you understand what the Hebrew term "ervah" means "fornication":
Deuteronomy 24:1 "When a man takes a wife and marries her, and it happens that she finds no favor in his eyes because he has found some indecency (ervah or fornication) in her, and he writes her a certificate of divorce and puts it in her hand and sends her out from his house"
He finds fornication in his wife when he marries her. This is what Jesus said the Law of Moses allowed for. We have a scriptural example of this law in effect pertaining to Mary and Joseph:
Matthew 1:18-19, "Now the birth of Jesus Christ was as follows: when His mother Mary had been betrothed to Joseph, before they came together she was found to be with child by the Holy Spirit. And Joseph her husband, being a righteous man and not wanting to disgrace her, planned to send her away secretly.
Joseph mistakenly thinking that Mary had committed fornication while they were betrothed to one another, planned to send her away. It says that he was a righteous man, so he must have been following what the Law permitted.
Also, If you want proof that "porneia" was the proper term for betrothal fornication, we also have a scriptural reference for that:
John 8:41 "You are doing the deeds of your father." They said to Him, "We were not born of "porneia"; we have one Father: God."
In this text, the Pharisees give a bit of a back handed sneer at Jesus, claiming that the was born of "porneia." This claim could be made by anyone since it is obvious that Mary was pregnant before her and Joseph were married. Therefore they are accusing Jesus of being born by sexual promiscuity before his parents were married (in the betrothal period). This is what Jesus said was the one allowance in the Law of Moses, and therefore must be what Deuteronomy 24 was speaking about.
Therefore, the "porneia" that Jesus said was an allowance for "divorce", was only to those under the Law of Moses, and only for the cause of fornication prior to marriage. Once the two were joined by God, there was no provision for divorce to the Jews, and especially to the Gentiles.