I am a single father with a 6 year old daughter. Currently I light three candles Friday night and my daughter will sometimes light one. At what point will she be old enough to light candles for the family? How many candles should she light?

The obligation of lighting Shabbat candles is on both the husband and the wife, yet the wife takes precedent over the husband. When she is not there the obligation returns to the husband. (Shulchan Aruch OC 263; 2,3,5,6 Har Tzvi OC1 140)) None of the children have an obligation (though by most authorities allowed in addition to parent) to light as long as they are dependant on the parents, and share the same household. You, therefore, are to continue lighting your Shabbat candles.