minors (ie those under 14) could not sign valid contracts (eg to sell land, enter into apprenticeships) nor could those under 21 marry without permission (tho any such underage marriages were licit) - normally on death of one parent then guardians were appointed by the church court (ie not the civil court tho until late 19th C the two were intermingled) from the deceased parent's family to protect any property brought into the marriage. If both parents dead then the same court would require next relations on both sides to care for the orphans - such guardians or overseers could appeal to the civil court (generally the Governor) for permission to dispose of property to support the child(ren). In the unusual case of orphans without any near relations on Island then I assume the General Sumner (as used for intestates) was involved - however this informal church based arrangement started to fail in early to mid 19th C especially following the influx of poor Irish after which charities stepped in with orphanages.
In your case there was probably no property to secure but also with no orphanages I suspect the guardian was someone who could support the child by employment - at this period the established church was acceptable to most tho Methodists had already established schools as did Roman Catholics around this period - I would expect any guardian would expect the child to attend the same church as their family or employees did.