If a child below the age of Bar-Misva experiences a situation of danger that for an adult would require the recitation of Birkat Ha’gomel – such as being bedridden with an illness, or traveling overseas – does he recite this Beracha?
The Magen Abraham (Rav Abraham Gombiner, 1633-1683), in Siman 219, cites the ruling of the Mahari Mintz (Rav Yehuda Mintz, Italy, d. 1508) that a minor does not recite Birkat Ha’gomel. In this Beracha, one thanks G-d "Ha’gomel La’hayabim Tobot" – for performing kindness to "Hayabim," which seems to refer to those who are obligated in Misvot, or who are deserving of punishment for their misdeeds. As a minor is neither obligated in Misvot nor held accountable for his wrongdoing, the Mahari Mintz contends, he cannot recite this Beracha.
Many others, however, including Hacham Bension Abba Shaul (Israel, 1924-1998), in his Or Le’sion (2:46), understand the word "Hayabim" in this Beracha differently, explaining that it refers to those who are "indebted" to G-d because of all the goodness He bestows upon them. Of course, this includes people of all ages, as all creatures are beneficiaries of G-d’s kindness. Hacham Bension adds that the accepted practice among Sepharadim is for minors to recite Birkat Ha’gomel, just like adults. This is also the view of a number of earlier Poskim, including the Hida (Rav Haim Yosef David Azulai, 1724-1806). The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) writes that this depends on communal practice, but Hacham Bension disagrees, and maintains that all Sepharadim follow the practice of children reciting Birkat Ha’gomel if they were in a situation that requires reciting this Beracha. This is the ruling of Hacham David Yosef, in Halacha Berura (219).
Summary: If a child below the age of Bar-Misva experiences a situation of danger that for an adult would require the recitation of Birkat Ha’gomel – such as being bedridden with an illness, or traveling overseas – then, according to Sephardic practice, he recites Birkat Ha’gomel, just as an adult would.