You can move your gallery installation by following the instructions here:
http://codex.gallery2.org/index.php/..._to_another.3F
You can move your vBulletin files without making any problems. Just move them over and edit your site URL in the Admin CP. I've done it many times.
As far as the attachments, I'd just disable them and have people upload them directly to the gallery. They can use image tags and just link to their photo
Edit: JohnMont has given me permission to upload his two gallery plugins... The first post has been updated.