If the child had been born while you were on the Student visa, they could have applied in the UK as your Graduate dependant. However if they were born under your Graduate visa there is no provision to apply as your Graduate dependant at all, including applying in the UK. A child born in the UK to someone with a Graduate visa can stay lawfully without applying for any visa, but if it leaves the UK it will need some sort of visa to return.
You will need to apply under a separate part of the immigration rules, not as a Graduate dependant. The relevant rule is Part 8: Family members, paragraph 305 "leave to enter [...] as the child of a parent [...] given leave to [...] remain in the [UK]".
https://www.gov.uk/guidance/immigration ... ly-members
If you were applying in the UK, it would be the FLR(HRO) form, but it is not clear to me how you apply from outside the UK. It's definitely possible, but I recommend professional advice to check how to apply.
The child was only eligible for free NHS treatment up to the age of 3 months, so if they have received treatment and not paid, that may need to be settled before a visa could be granted. I recommend professional advice about that aspect too.
I do not give immigration advice. I refer you to Immigration Rules, guidance, other online content and to your sponsor.