For a very young child (pre-literate) who is deaf and does not use spoken language I think a medic-alert type bracelet might be a reasonable option..
I would state on the bracelet:
The child's FIRST name and Last initial (JOHN S.)
That they are deaf
They use "American Sign Language"
A contact phone number "please call (111) 111-1111)"
I would NOT:
use the abbreviation "ASL" (versus "sign language"/"American Sign Language") - because not all hearing people know what that abbreviation means)
I would NOT put a home address, or a great deal of identifying information on it (do NOT put a SIN/SNN number, house address, full first middle and last name etc)
I WOULD also suggest putting some identifying "detail" on the bracelet ... it might be a symbol (logo/animal etc) or a "code word" (it could be anything: fav team, colour, birth month, etc) , located somewhere "discrete but visible" on the bracelet that allows the caller to "prove" they have the child. (You can ask "on the bracelet there is a word/symbol/logo etc located "x" please tell me what it is, as a security precaution)
I do think that once a child is old enough to write (and read basic things like "are you lost" and know to head for a cop/uniformed worker etc) that the bracelet should be the child's choice.
If a child has a CI or other implanted hearing device or other medical device then I would recommend that the bracelet be worn always (just like a pacemaker one, shunt etc) ... espeically due to the steps that need to be taken if an MRI is needed etc (the make and model of the CI should be listed)
HTH