That should definitely be accepted. Traditionally in English (as in all Germanic languages), one uses the neuter "its" with nouns like "child". Nowadays, there's a tendency to either go with the sex of the child, or use a gender-neutral "their", but the traditionally correct form should at least be permitted.
I would never refer to a person (adult or child) as 'it' unless they actually asked me to. I think it is exceptionally rude and would always use 'they/them/their' if the gender is unknown.
People who claim that it's wrong to use this as a singular pronoun probably use it all the time without noticing. For example, if I said "Someone from the office called for you," I don't think anyone would, in real life, respond with "What did he or she say?" rather than "What did they say?"
Yeah, technically it might be grammatically incorrect, but it has a long history of use, dating back many centuries. A lot of people object to the use of gender neutral they, but almost everyone uses in such sentences as "if anyone calls, tell them I'm not home." And as kokiri85 mentioned some people, myself included, use they/them/their in reference to themselves. Someone reference me would say something like "i really like their shirt"
Curious - does anyone else have a hard time hearing the difference in the synthesized voice between "barna" and "barnet"? I frequently mix them up. Though I suppose in this case I should have known the answer was "barnet" because "sin" indicates the subject is singular :)