Its clear that you feel, you want to help in some way, which is very kind but How does your DD feel? At 10 she's quite young to take on that role.
I think it might be putting a lot of pressure for her to feel she has a role, has to step up and behave in a certain way, as its hard to know what that role is and whether it would be welcomed because grief can be so irrational and contrary. Even when people know its with the best of intentions.
I think it's better that you as an adult can judge how to help the friend, maybe knowing that there will be invites to tea after school in future, and so on would be easier on both than a formal greeting at a such an emotional funeral.
Your DD's friend will still feel supported with a kind message and the knowledge that you will both still be there for her in the longer term.
As to attendance. It really depends on the family and the type of funeral. Some can be welcoming events, some can be very difficult. Also depends on how the bereaved child feels. Perhaps she wants her grief to be private on that day and may not want a school friend there.
It is very difficult to predict how people might feel at that exact time. At a close funeral I remember a distant cousin coming up and chatting to me as we walked to the grave site. He thought he was being really nice and he was but I just wanted to tell him to shut up and go away. I wanted to be alone with my thoughts at that time and felt it was really intrusive, having to be polite when all I wanted was a few moments to think.
So I think The most important thing is that your DD's friend feels she has a kind friend in her radar the day afterwards... and day after that, when all the fuss and attention has died down. Its the long term support that matters. That might be easier for your DD too.