EEA Family Permit???

hi there, I was looking for some general advice about my family situation and our eligibility to apply for an EEA Family Permit...

Our situation:-

My girlfriend is an Ecuadorian national (holds an Ecuadorian passport) she has been living in Italy for the last 16 years with permanent legal residency. She has a valid, genuine Article 10 residence card that was issued under EU law through her mother having Italian citizenship. My girlfriend is still awaiting her Italian citizenship application to be processed.

I'm a British Citizen, born in the UK to British parents and living in the UK. My girlfriend and I have a 3 month old child together, the child is living at my home in the UK and she has British Citizenship by descent (a British passport has been issued).

My girlfriend is currently visiting the UK staying at my home on a 6 month visit visa but she would like to return to Italy and apply for an EEA Family Permit under 'Derivative Rights of Residence' rules because she is the primary carer of a British child as the child's legal guardian.

I'm able to financially support both my girlfriend and the child in the UK, they would be living at my home and there would be no strain on public funds.

Please can you advise if we have a case to apply for the Family Permit under 'Derivative Rights of Residence' rules and if so what areas of the application will need some emphasis to support the application?

Many Thanks...