I am so very sorry for your loss and all you are going through. This is so much for you to manage right now.
I think you've gotten a lot of good advice so far. Definitely get any help you can from friends, family, church, work, etc. Anywhere you can. And ask the pediatrician or even her school may have a list of references of places to get any help you may need.
I worked as an elementary school counselor, so I have some experience in this area (although not with kids as young as 3). I think you explained things well enough now. Expect her to have more questions here and there both now and in the future. She may ask questions out of the blue, but it just means it's on her mind at the time. As she matures and understand things differently, it may prompt more questions. It's always best to answer with simply with basic information and allow her to ask more questions if what you've said wasn't enough.
Don't be surprised if she doesn't react the way an adult would to death. Kids process and grieve very differently.
Also, either now or as she grows a little, books may help explain some things. There are many titles out there. Ask the pediatrician, the school or anyone else you know who might have knowledge. Even an internet search and/or a trip to the library would help.
I hope you've gotten the help you need here. Again, I'm so very sorry for your loss.
B.