1) Back up your device through iCloud or iTunes. When you restore your backup to your new device, your Giffer library will also be restored.
2) Copy all of your gifs off of your device through iTunes file sharing: Open iTunes and click on your device's icon. Click "Apps" on the left and scroll down the main window (not the "Apps" list) until you see "File Sharing". Click "Giffer" then drag the "gifs" folder and the "giflibrary.archive" file to your desktop (or wherever you want to back them up). Restore your library on your new device by again clicking "Giffer" under "File Sharing" and simply drag the "gifs" folder and the "giflibrary.archive" file from your desktop (or wherever you backed them up) into the same file list area that you dragged them out of.
Of course just to be on the safe side you could always backup using both of these methods.