Q. What is the reason we do the chalaka of a 3 year old on Lag Baomer?

A. It could be that this was done with the intention of being mechanech, educating and starting off the child on his very first mitzvos at a place that is a source for tefilos and is a Mokom Kodosh.

One may add that the kever of Rashb”i was chosen in these generations, following what Rava points out in Talmud (Makos 17b) that women should strive to have children that are comparable to Rabbi Shimon Bar Yochai. It could also be that Rabbi Shimon gave an opening to return for people who are not yet Baalei Teshuva by upholding the opinion that “dovor sheino miskaven” (an unintentional act) is sometimes permitted. That would explain why this festive occasion became so popular even by the yet non-religious.
The Chalaka would then be done on Lag Baomer the day his yorzait or the day he came out from the meara.(See Minchagei Tispores Rishono p.125, Hakoton Vehichosov p. 58, Nitey Gavriel – Pesach 3: ch. 58)

Horav Shlomo Miller Shlit”a pointed out that traditionally some would do the chalaka at other k’vorim of other tzadikim such as the kever of Shmuel Hanovi. He also made reference to the Medresh (Tanchuma – Kedoshim 14 and Yakut Shimoni ibid.615) that compares a child to the mitzva of Orlo, where after the first three years you enter the fourth one designed as “Kodesh Hilulim.” That being the time of his beginning in chinuch for mitzvos he can now perform. (See similar opinion in Arugas Habosem O.H. 210)

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a.