First of all, it's worth noting the this work is not the first century Didache, which also goes by the name "Teaching of the Twelve Apostles," or even the third century Didascalia Apostolorum. Instead, it's an ancient Syriac document, typically dated to the fourth century (see, for example, Witakowski), which is about the same time as the writing of the Apostolic Constitutions.
The same translation of the work is available with commentary in Pratten's Syriac Documents, which sheds a little light on your questions.
First, regarding the date, this is indeed January 6, as Pratten writes in reference to the "latter Canun":
January: the Jewish Tebeth. "The former Canun" is December, i.e. Chisleu.
As for other holidays, it's not immediately clear why only this one appears – not even Christmas is mentioned, as Pratten notes:
See Ap. Const. v. 13, where Christmas, of which no mention is made in these Ordinances, is called "the first of all," the Epiphany being ranked next to it.]
Chapter 5.13 of the Apostolic Constitutions places Christmas first, then Epiphany, and then Lent:
Brethren, observe the festival days; and first of all the birthday which you are to celebrate on the twenty-fifth of the ninth month; after which let the Epiphany be to you the most honoured, in which the Lord made to you a display of His own Godhead, and let it take place on the sixth of the tenth month; after which the fast of Lent is to be observed by you as containing a memorial of our Lord’s mode of life and legislation.
So it's not surprising that Epiphany would be considered above Easter or Pentecost. But what about Christmas? The likely reason for the text's apparent disregard of it is that it viewed Epiphany as celebrating all aspects of Christ's birth and early life. This was apparently common in Syriac writings; for example, Epiphanius quotes Ephrem the Syrian as saying:
Thus the advent of our Lord Jesus Christ, his birth in the flesh or perfect incarnation which is called the Epiphany, was revealed... (source)
For more on the history of Epiphany, see Wikipedia's helpful treatment; it confirms many of the details I've found covered in works like the Encyclopedia of Ancient Christianity.