Where does the idea of making a kiddush (party) Shabbos morning when a girl is born come from? How far back does this practice go?
** hope you'll understand my english :) **
It seems there's no formal Mitzva or Halakha for making a party in this situation, but something that was formed over the medieval times. A little more about it you can read here:
I'd like to add (from the Hebrew Wikipedia of Zeved habat) that the source of the word Zeved (which means present/מתנה) comes from Genesis (Parashat Vayeitzei)- where Leah used it after she gave birth of Zebulun:
כ) וַתֹּאמֶר לֵאָה, זְבָדַנִי אֱלֹהִים אֹתִי זֵבֶד טוֹב--הַפַּעַם יִזְבְּלֵנִי אִישִׁי, כִּי-יָלַדְתִּי לוֹ שִׁשָּׁה בָנִים; וַתִּקְרָא אֶת-שְׁמוֹ, זְבֻלוּן
(20) And Leah said: 'God hath endowed me with a good dowry; now will my husband dwell with me, because I have borne him six sons.' And she called his name Zebulun.
Now, according to the Masoret Dina was born with Zebulun, and that is why we find a clue in the word Zeved for both (Zebulun and Dina)- at least in Hebrew (letters זב from זבולון and ד from דינה).
Hope it was helpful :)
Edit: As response for the comment of the post's writer- I found this source בית אהרן וישראל (in Hebrew) which contains an article called: "Source of making Kiddush on Shabbos where a newborn girl gets a name"; מקור למנהג עשיית קידושא רבא בשבת שקוראים שם לבת הנולדת)-- on pp. 128-129 (by Rabby Gutfreund).
Now, I'm not so sure I completely understand his article--and if someone want to edit my answer, please feel free to do it--
but according to him, it seems that people used to have Kiddush on Shabbos after giving the new baby girl a name. In addition to other reasons, he says that the 'Naming' process and the Kiddush set to Shabbos, because "people are at their homes" ("העם מצויים בבתיהם"), i.e., it's convenient. At last, he wrote that there's a connection/dependence between Kiddush and the 'Naming' process, such that some people are not giving a name to the baby until it's possible to make a Kiddush (and of course that can happened only on Shabbos or Yom Tov etc).