The quote is a horrible distortion of what the Talmud is actually discussing and completely ignores the context of the discussion.  In no place does it say that such an act is permitted.

First, there is some background that needs to be presented.  

Until Biblical Law, it is forbidden for a man to have sexual relations with a woman who has had any of several different types of vaginal discharges.  The one under discussion here in the Talmud is called “ziva” and is covered in the Bible in Leviticus 15:19-33.  A woman who has such a discharge is called a “zavah” (a man who has a similar discharge is called as “zav”), is ritually impure (i.e. they cannot eat sacrificial/holy foods, nor may they enter the Temple area in Jerusalem).  Furthermore, a man who sleeps with a zavah also becomes ritually impure as well.  The status is zavah is removed when the discharge stops, she waits an appropriate number of days without seeing any more discharges, and then immerses in a mikvah.

Over the years, the Sages have implemented various decrees on Jews to prevent intermarriage with non-Jews.  One of those decrees was to declare that non-Jewish women have a presumptive status as a zavah.  Since a man who sleeps with a zavah becomes ritually impure himself, it was hoped that by declaring this, it would help prevent Jewish men from associating with non-Jewish women.

There is a general rule in the Talmud that the sexual acts of a minor are not considered sexual acts until they reach a certain age.  For males, that age is nine and for females that age is three.  Having sexual relations with them prior to that age is certainly forbidden as an assault, but it does not trigger any of the attendant consequences that come with having sex.  For example, if someone (God forbid) had sex with a minor girl under three, she would not be rendered a non-virgin.

With all that said, let’s get to the conversation in Avoda Zara.  The discussion, which starts earlier on 36, talks about various methods and decrees that were used to prevent premarital sex both between Jews and between Jews and non-Jews.  One of those methods that was mentioned was the rabbinic decree that non-Jewish women have the status of a zavah.  

Here’s the actual quote (starting from earlier on 36b):

All that is being discussed here is at what age this presumptive status of a zav or zavah begins, and the answer is that it begins at the age when their sexual acts have the consequences of sexual acts — nine years old for a male, and three years old for a female.  If a man (God forbid) has sex with a gentile girl under three, it is, again, certainly forbidden, but since she is not a zavah, he does not become ritually impure as he would if she were older or an adult. 

Nowhere does the Talmud say, however, that one can have sex with a gentile girl if she is three years or older.  On the contrary, to say so completely ignores the entire context of the discussion, which is that the Sages were making it *more difficult* to have sexual relations with non-Jews of any age.