As you''re unmarried, the default position is that each of you would leave with the assets that are in your names. This is particularly relevant for the savings. If savings are in joint names then the reality of it is that whoever withdraws them first will probably get to keep them. If they''re in your own account, they''re yours.
If your girlfriend were to be the main carer of your child after separation then she could potentially apply under Schedule 1 of the Children Act for a financial order for the benefit of your child. This could potentially include a portion of the equity in your home.
She could also apply, regardless of who is the main carer of your child, under the Trustees Of Land and Appointment of Trustees Act (TOLATA) for a share of the house, but she would need to prove a ''beneficial interest'' in the property, which is quite difficult. This is a complex area and probably beyond most posters on this forum.
If you''re in the process of separating, or have already separated, why not look into
mediation to resolve where your child lives? It needn''t be an either/or decision, as your daughter can spend a significant amount of time with each of you, maybe even 50% of the time if that suits the three of you.
One question that sticks out is where your girlfriend is from? Would she be looking at leaving the UK, and would she try to take your daughter with her if she did?