This is one of my favorite books, and I've been thinking about this question for a few days now. My opinion is that the book holds many important ideas, and it is difficult to say with any certainty what the author intended his main idea to be. Since the book was intended as a children's story, an adult interpretation may be a stretch.
First, this book features a "perfect" society, one which celebrates the diversity of many different countries and cultures, one in which everyone cooperates and takes equal responsibility for the good of the community. There seems to be no dissension at all. So, one main idea for this story could be the author's idea of what constitutes a Utopia.
Second, a point of the book could be that for all the millions in wealth that this community has, in the way of diamonds, the community is actually trapped by its own wealth, confined to a volcanic island in the middle of nowhere. The denizens cannot take too many diamonds to sell, or the diamond market, based on supply and demand, will collapse, making diamonds virtually worthless. They must be careful to not flaunt their wealth when they visit the mainland, or they will attract dangerous attention. The only people they can show off to are one another. And no matter how wonderful these people are, it is a very small community, after all, with no stimulation from outside. So, a message could very well be that great wealth can confine and trap people.
Third, in spite of the intelligence, creativity, and cooperation of this community, they are nearly destroyed by the volcano when it begins to erupt. No matter how much wealth we have, it cannot always insulate us from natural occurrences.
Fourth, I have always had the impression that the author was poking a little gentle fun at the balloon crazes of the late 19th century and of the adventurers who boldly set forth for the Geographical Society. People really did seem to have "balloon fever" for a while. Nelly Bly, a famous reporter, captured the world's attention when she managed to beat the fictional hero of Around the World in Eighty Days, who traveled by balloon, by a matter of about a week.
Finally, it is entirely possible that du Bois simply set out to write a wonderful adventure story. And if this was his only intention, he did a wonderful job. I pretty much required my own children to read this book, and I wish it were more popular today.