I had a memorial service rather than a funeral. I invited anyone and everyone who cares about me, Millie, or my family and we ended up with a large number of people. I was happy about that because I felt like I was sharing Millie with them in a way, something I won't be able to do now. Millie's body wasn't at the memorial service. We had a viewing up at the cemetary after, but I wish I hadn't done that as she looked nothing like she did when she was alive. At the actual moment of burial only close family was there.
I attend a Unitarian Universalist church and had the service there (although you don't have to be a member to have a service there). Other than the eulogy, I planned the entire service. They are quite open to non-religious readings and songs. I found two wonderful poems that served as the readings. One of them might be meaningful to you. It's titled "The End" by Rabindranath Tagore, an Indian poet and mystic. I bet it's copyrighted so I won't reproduce it here, but would be happy to send it to you. One of the songs I chose was "How Could Anyone?" (not religious). It was in our hymnal but it's also on Itunes and if you google the song and artist's name (Libby Roderick)you can find the lyrics. It's simple and beautiful and very fitting for our little ones who were with us so briefly.
As for burial- Millie is buried in the baby section at the cemetary I chose. For now I wanted her to be with the other babies. At the same time I purchased my own burial plot (Millie's father is no longer involved) and had it written into the purchase contract that when i die she will be disinterred and buried in the same plot as me. She will have her own headstone, but it hasn't arrived yet.
I hope my ideas spark some ideas for you. I like your plan to do this on his due date. I would like to do something for Millie on her due date too, but I don't quite know what yet.