Practical advice.
A 4yo who has just started school.
Be nice to the people in the school office. Do you have anything official to wave at them (e.g. from SS ?)
You'll need to ask the school for the new parents info they will have sent new starters so you are up to speed with info, and make sure you are down as carer for emergency contact etc.
She will be learning to read and they may want you to read with her daily. They may also want you to practice counting, and colouring in.
You'll need to find out how they deal with PE kit and stuff.
Try to get to know some other Mums at the school gates, even if only 1 or 2, as they can point you at info and help with routines or whatever. You'll need to know what to say so 'DN's Mum isn't well so DN is living with me right now' or something.
She'll be very tired, so in the absence of other info try lights out time of 7:30pm (bath, teeth story, lights out).
Going from zero (or 0.5 in your case) to a 4yo is a big step. Make sure you keep reassuring her about Mummy and it's not DN's fault that mummy got ill.