Right to Reside - EU National with child

Client is a Latvian National with a child born in the UK, whose father is British.  Child is too young to be in education.  She has never been married to the father and he is not involved in supporting or bringing up the child in any way - it was a very brief relationship from what I can gather.  She has not been here 5 years and does not have right to reside via any other family members etc. 

My understanding is that she cannot derive a Right to Reside via the baby - am I correct?

She has tried to claim JSA several times but tells me the claims line say ‘you have status to claim Income Support’ but I think what they mean is that she is a lone parent of a young child, not that she has right to reside status.

I agree that is what she should do and that is what I have advised her I think is going to be her only option - but just wanted to check I hadn’t missed some route into Right to Reside that could have helped her.