In Paper for iOS you can only export as large as your iPad’s native resolution. If you care about getting more pixels out of your Paper art then an iPad Air is the way to go.
To get the best quality image out of Paper I export to the iPad’s camera roll and then transfer it with either iCloud’s Photostream or Dropbox. For an untainted image without the eggshell background tapping the Camera Roll icon brings up an option toggle the background off or on. When toggled off you will end up with a PNG file with a transparent background (if you didn’t fill with another color).
These uncompressed PNG files are the way to go if you plan on further manipulating them in Adobe Photoshop or one of the other applications in the Creative Suite.