Congratulations, Megan, on your upcoming honeymoon to WDW!! How exciting!!
You are absolutely correct that you can get a Newlywed button during your visit to WDW. The button is free, and is your to keep. I believe the current version says something like "Happily Ever After" (cute, huh?!). You don't need to bring any proof/verification, just ask for a button at guest services at any of the parks, or at check-in at a Disney resort (they
usually have pins, but not always).
If you want to see the button in advance, click
HERE to see examples of all of the buttons offered to guests at Disney World (it's a small picture, but I think you'll get the idea). Also lots of other helpful ideas on this page for adding some more magic to any celebration at WDW, if you are interested.
Hope you have a great honeymoon at WDW!!!