In a separate suitcase or carry on most of the time depending on the dress volume. Fold it an vaccum pack it will save you space.
The wedding I had attended in Bora, I believe the dress had been sent to the resort in advance (through mail, etc.). That would also allow for easier/less stressful travel...but I would definitely recommend setting that up well in advance if you plan to go that route.
I would be more stressed sending the dress through the mail than possibly having to check an extra piece of luggage to get it there. That way, it will likely cost less and more likely make it there.
If small enough, I believe you can just hand it to a flight attendant so they can hang it on the plane. I certainly would not ship it as there is always a risk it might get "lost" at customs:-)
I was searching for another topic and came across this in a trip report.
Brides, for your wedding gown carry it with you in a garment bag. We used Wally Bags 66" Gown Length Destination Bag and it carried both my wedding gown and my husband's suit as well as my shoes and accessories. Air Tahiti Nui hung it in their storage inside the plane for us and then Tahiti Air did the same on the way to Bora Bora but stored it in the cargo at the last minute as we boarded to keep it safe on the way back.
You can definitely take the dress if it is your carry on or packed into your luggage.