Absolutely, positively do not move your Zotero folder into the Ubuntu One sync folder. The Zotero folder contains the Zotero database - zotero.sqlite - and syncing that via sync services like Ubuntu One, Dropbox etc. will very likely lead to database corruption. There are dozens of threads on the Zotero forums of people who wanted to save a couple of bucks by doing this with dropbox and ended up with a hopelessly corrupted database.

Ubuntu One does not support WebDAV, so that's out.

You can put just the storage folder within the Zotero data folder into Ubuntu One. I believe it's possible to designate that folder to be synced by Ubuntu One, otherwise create a symlink to it in the Ubuntu One sync folder. This will allow you to back-up files online and sync them between different computers, but as opposed to syncing through Zotero storage, you won't be able to access the files through your library at zotero.org, nor will you be able to share files in groups.