In Irish, there is no verb for "have". Instead, something is "at" you. So when you see a form of bí used with ag, you have to check to see if it's 'have'. Here, you have agat, and the subject placed between. So it literally is: "Is a child at you?", or "Do you have a child"?
The configuration, where there is no word for 'to have'; instead, you say something like 'with me there is'; is cross-linguistically common. That configuration is used also in Welsh and Hindi (in both cases, i learned that by practising those languages on Duo); and also Finnish -- i know; i was born in Finland and speak Finnish. However, Chinese, Greek, and probably most or all Romance or Germanic languages, have a word for 'to have'.
Irish and English are both perfectly capable of indicating the difference between a single child and multiple children.
This sentence is definitely only asking about a single child. Indeed if you were not interested in the number of children that a person had, you would ask An bhfuil clann agat?.