Oh OP, my heart is breaking for you. My gorgeous dad died in April at only 70 years old, it was half expected but he was so strong and had always recovered previously so I think we all expected him to get better this time but it was not to be. A few points for you.
DD will feel something is wrong and will likely understand nana is gone. My DS3 kept asking if grandad was coming home from hospital for a while and there was a change in his behaviors, he became quite aggressive and emotional. Please be patient with her as she will not fully understand what is happening. Also, in the moments of darkness, she will provide strength and light for you. DS truly saved me from utter despair, in such a way that only one so innocent can. Even in utter heartbreak my DS made me laugh and, of course, they keep you busy!
Talk about her, she has left you with a lifetime of wonderful memories and love. These will keep you going in the darkest of times.
Work can wait. I started a new job 5 days after dads funeral. I had no choice financially but I know now I needed more time. I can't emphasize this enough OP, this is a time for you and your family. You must prioritize yourselves at this point. My DSis is a Midwife and has not long gone back. I wish I had had the option.
Your family are number 1. Be with them, support your dad. Everything will be full on with practical tasks, arranging the funeral, informing agencies etc. Take time as a family, even if just to cry. The hard work starts after you lay your beloved mum to rest, the loneliness and foreverness will kick in and you will need each other like never before.
Eat properly and ensure you sleep when you need it, grief can cause you to eat crap which will make you feel worse. Eat the cake but ensure it is not all you eat.
Take the help, we wanted to do everything for mum (and dad) but it is too much and leads to utter exhaustion. If aunty x wants to do the dishes let her, uncle y can take the bins out.
Finally, take time to just be. Think about her, laugh, cry, talk to her, look out for signs from her. ( I'm not woo but have definitely felt dads presence when I needed reassurance).
Take care if yourself OP, remember all the things your mum did for you and taught you and you will realize she is never truly gone, she has left an amazing legacy in you which you will now pass on to your DD.
Lots of love ❤️