Solution 1:

Your dependent or ward (credit to amcnabb), both of which are legal entities, but both of which apply outside the legal sphere.

Dependent connotes a relationship in which the guardian is both provider and protector, whereas ward implies that the guardian is the protector, but not much else.

Solution 2:

I like charge:

: a person or thing committed to the care of another

from wiktionary:

The scope of someone's responsibility.

The child was in the nanny's charge.

Solution 3:

A traditional word for this would be "ward" (for example, in Dicken's Bleak House).