When Rivka comes to Yitzchak’s home the Torah tells us “Vayive’ha Yitzchak ha’ohela Sarah imo vayikach es Rivka vat’hi lo l’isha vaye’ehaveha”, Yitzchak first brought Rivka into the tent of his mother Sarah, and then he married her and loved her. Rashi explains that there were three miracles that were always present in the tent of Sarah – the dough was blessed, the candles remained lit from erev Shabbos to erev Shabbos, and a cloud enveloped the tent. Despite all the miracles which Eliezer related as having occurred on his journey, Yitzchak did not take Rivka as his wife until she proved capable of duplicating the miracles of his mother Sarah.
The Lubavitcher Rebbe (Likutei Sichos vol.15, see here) notes that the assumption of Rashi seems to be that Rivka performed the mitzvah of hadlakas neiros Shabbos even before marriage (see the footnotes of the sicha which discuss whether an arusa is chayeves in hadlakas neiros), even (according to Rashi’s chronology) from the young age of three years old. I have not noticed it lately, but I do recall years ago Lubavitch actively campaigning to have all women, even little girls, participate in the mitzvah of lighting neiros Shabbos.
Regardless of the merits of this proof (might the hadlakas neiros here have been a test of some sort and not simply a kiyum of ner Shabbos?), there is a custom in many homes of having girls light Shabbos candles. The minhag is brought by the Aruch haShulchan, and I have seen quoted in a number of places that this was the practice of the Brisker Rav. My older daughters (11, 8) do light candles, but not my 5 year old. Assuming the hadlakah is a kiyum of mitzvas chinuch, I am not sure a three or five year old is ready for the mitzvah yet (especially using matches and a candle), so in our house we wait for the girls to get a little bigger.