On what basis has she made her EEA application? Was she in a relationship with an EEA citizen?
You could try and make an application as an unmarried partner but to get over even the first hurdle, you will need to show that you have lived together in a relationship akin to a marriage in the UK for at least 2 years or outside of the UK for at least 4 years. You will then have to demonstrate that you can afford to maintain and accommodate her without recourse to additional public funds.
The main problem that you will have is that she has no existing leave (subject to the EEA application and the basis on which this was made, I will need for you to tell me more about that in order to advise on that aspect). The application would need to be made on form FLR (O) which currently carries a fee of £550 but which is going up on 6 April to £600. You will need to try to convince the Home Office that there are compassionate or human rights reasons why the application needs to be made from here and why she shouldn't have to go back to her home country to make an entry clearance application. The fact that you have a child together strengthens her application and there is much case law which highlights the importance of the rights of children, in particular those that are British. The application will be discretionary and so I would advise that you seek the assistance of a solicitor to help you make the application and include all the necessary case law.
I hope this is helpful in which case please accept. If you require anything further, please do not hesitate to ask.
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