We didn't do a dedication ceremony, but our local council has a day every year where families with a baby born in the year can plant a tree. The tree is planted in parkland areas (quite a lot of bush/parkland in our area) with a little plate with the babies names and date of births on it. It's become a big event now.
But I think the idea of planting a tree is great and it is something you can show your child when they are much older. Perhaps you could make that part of your day.
HTH