Yeah, you're going to have to take multiple screenshots, and put them into some kind of .gif animator. I agree that it'd be easier to find a place with a smoother, less busy background if you can.
I've tried something similar with World of Warcraft, which I assume is similar to Neverwinter Nights. There is actually a program out there called WoWModelViewer, that has all the objects/characters/armor sets from WoW and renders them for you, and even animates them on any background you choose (including transparent.) You can customize the render to make it match your character. Depending on the popularity of your game, there may be something out there like WoWModelViewer, which would make your life a LOT easier.
I find that grabbing screenshots in-game do not make the best image files, so you may end up a little disappointed with your gif's quality.
Good luck though, and be sure to show us the end result!