If you do find an old backup to restore to, you could first take a backup of the current state of your iPad and copy it so that you can restore back to it after you've taken a copy of the photo - on a Mac backups are stored under :
Mac:~/Library/Application Support/MobileSync/Backup/
The "~" represents your Home folder. If you don't see Library in your Home folder, hold Option and click the Go menu.
So after taking a new backup copy that folder somewhere else so that you have a copy of it (e.g. external drive, flash-drive) just in case it gets overwritten after restoring to an old backup or by time machine.
If you find and restore a backup with the photo in it you could copy the photo off the iPad (on a Mac Image Capture, iPhoto or Aperture should be able to copy off Camera Roll photos), copy your new backup back into the backup folder, restore to it, and then email the photo to yourself and save it from the Mail app to the Camera Roll album.