When my eldest turned three her male cousin also turned three. Many of her friends and her cousin were getting Tzitzit. She asked for her own. We explained that boys wear TzitTzit and girls light Shabbat candles and therefore we adopted the custom of our three year old girls lighting one candle starting when they turn three. This worked (and continues to work) for us, however, where did this custom come from and why is it not prevalent?
There seem to be different views.
On the one hand Chabad are solidly in favour, see here. A reason is suggested why the custom is not prevalent.
On the other, Rabbi Eli Mansour at dailyhalacha.com says “…Therefore, the prevalent practice is that the unmarried daughters living in the home do not light Shabbat candles, and instead rely on the mother’s lighting. An unmarried girl who insists on lighting should certainly not recite a Beracha.”
Rabbi Elchonon Feldman of Belmont United Synagogue explains here that “whilst every family has different customs in regards to lighting the Shabbat candles, young ladies and girls all play a part in this Mitzvah.”
It’s a classic CYLOR.
The three varying minhagim that come to mind for this are: starting at 3, starting at bat mitzvah age, and starting when one is married.
Since I am most familiar with the minhag of age 3 which you have adapted that is the one I will explain... when one considers the importance of chinuch it makes sense that one should start before the age of bar mitzvah. Why age 3?
Three is considered a milestone in a persons life in which one becomes a child and children must be taught right from wrong as well as the traditions they will carry on throughout life. Successful enculturation (chinuch) must start when one transitions from infant-hood to childhood.