W.L.
We have 4 children and 2 years ago we had 2 Great Grandmothers pass away in 2 months right after #4 was born. We also had the last Great Grandmother pass away this year.
We have also had a classmate die during a daughter's Kindergarten year. As you can see, we have experienced talking to our children about death quite a bit. Each time, we have always had one of our kids at the age of 3, like yourself. This is such a personal topic, but my opinion is that you really must address this with your daughter. You need to help her have closure and understand what happened, even if it will be hard on her. Part of our discussion with our kids have included the following: In life we are all born and we all die, we are so sad when our loved one dies because we won't be seeing them for a long time, but we think about all the happy times we had with them when we are sad. They are going to a happy place where they won't be hurting anymore and the wonderful thing is that they will be waiting for us when we go there too. We look through pictures and talk and pray about the person for a handful of time too. I have explained that at the funeral, people will be crying because they will be missing them and thinking about all the happiness the peron brought to their lives. It's ok to cry and it's ok not to cry. Dad and I want to hold your hand and hug you if you want us to. The person who has passed doesn't want us to be sad for a long time though, they want us to be happy and remember them.
I know some of the above has religious undertones, so take it for what it's worth. I have been extremely surprised how a funeral has helped my children have closure. If you feel strongly about not taking your daughter, then maybe get a babysitter, pick up your daughter after the funeral and have her surrounded by family for at least some time and tell her that is a way of thinking about how special your loved one was/is. Best wishes in taking this on and I am so sorry for your loss.