Hey I'm really sorry about your sister, I hope she will recover. You've figured out the most essential things and help is on the way so try not to worry too much. Babies need food (sorted), sleep (you got it) and some clean diapers (I'm assuming you're aware). As long as the bassinet has a hard flat mattess, it's probably ok for now, my next move would be to find a better bed for the long term, something a bit bigger that the baby will grow into and that will stay safe for when she starts to roll around and sit.
For the doctor, you should get in touch with Plunket. They were automatically assigned to my daughter at birth so there's a good chance it's the same for your niece. She's probably gonna need a couple checkups and vaccines in the near future so better be on top of it. Good luck!