Does one need to recite Kaddish for an unborn child? A google search produced only references to an unrelated book.
Kaddish is said as a merit for the deceased to shield him from the judgement of Gehinnom. If the deceased were not required to undergo such judgment (e.g. he was a complete tzadik) Kaddish would not be necessary, but is nevertheless said even for a child once he reached the age of understanding what a sin is. (Mourning in Halacha 39:29-30) based on Sdei Chemed (Aveilus 151), Pischei Teshuvah (376:3),.
For an unborn child, the child is a pure tzaddik who never experienced any sin and Kaddish is not said.
Kaddish is part of the laws of mourning, which weren't instituted for the loss of an unborn child. (In fact, if a baby was born with severe medical problems and left this world soon after entering it, most rabbis would advise against shiva, kaddish, and the remaining mourning rituals.)
It's a sad and difficult situation, especially without the usual routines and recognitions of mourning. I suspect that when these laws were instituted, the state of women's health was such that they couldn't afford to go through full mourning for a lost pregnancy. (The Talmud has stories of people discussing plans for their newborns, with the caveat "assuming this one makes it.") Hopefully you find a good support network, a competent rabbi included, to be there for you. May God give you strength.
Kaddish is usually said for someone for whom there is an obligation to sit shiva. We see this in the original source for saying Kaddish for the dead, The Ohr Zarua (II:50), who quotes the Medrash: "Rabbi Akiva saw a strange and afflicted man who told him that he has been dead for many years and because he was particularly sinful in his lifetime he was judged harshly. When Rabbi Akiva taught the man's son to say Kaddish the man was spared the punishments”.
Thus, we see that origin of the practice to recite Kaddish was said within the context of the chiyuv aveilus. (But being that it is not obligatory law within the laws of mourning, it can be recited by others as well)
For an unborn child or a child that died within 30 days old, there is no requirement to sit shiva, they under the halachic classification of a "nephel" ie. a non viable baby, meaning the baby was not considered alive in the utmost halachic sense (although its death does require a full jewish burial, see Avoda Zara 42a,REMA (OC 526:10, HAGAHOS MAIMONIYOS (Hilchos Milah 1:10) and the BI'UR HA'GRA (OC 526, and MAGEN AVRAHAM (ibid) and CHAZON ISH (OC 133:2) as well for a fuller discussion of the requirment to bury a nefel).
Therefore Kaddish is not said for them.
Rav Yitzchak Zilberstein of Ramat Elchanan says that one may recite Kaddish and other aspects of mourning for a baby of 30 days and beyond. But not less. Perhaps one could extrapolate from that, that a baby less than 30 days, no Kaddish is recited:
צדוק הדין וקדיש נוהגים לומר אפילו בתינוק בן שלושים יום ומעלה ולא בפחות. (גשר החיים י"ב י"א) ומנהג ירושלים שאם יש מנין על יד הקבר אומרים שם קדיש על תינוק בן שלושים ומעלה, וגם בבית האבל אומרים קדיש ומתפללים (ויש נוהגים אפילו בלמוד משניות) הגם שקטן ודאי נקי מחטא, ומה מקום להתפלל עליו? אפשר לומר, מי יודע איזה בעל נשמה היה הקטן (ואולי חטא בגלגול קודם). גם עושים מנין בבית האבל בשביל האבל שיוכל להתפלל בציבור.