I think the problem here is your 1&1 nameserver not accepting entries for the new domain, as it hasn't been bought through 1&1.
The answer is to use the DNS that is running on your Plesk box. Configure your new domain NS entries to by ns.yourdomain.com where yourdomain is a domain that you already host. The DNS on your server will be configured to resolve all the domains you host.
What happens is that when someone wants to see your website, they ask the master DNS servers, 'who can tell me where this domain is', they return the NS that you entered into the domains NS boxes.
With 1&1, the nameservers are not returning anything as they do not host the domain - normal behaviour - you wouldn't want anyone to stick any old domain on your DNS server after all. Now, as you have a DNS server that is hosting these entries (your plesk box), you just need to tell the domain's registrar.
You might run into a problem here if the 'virtual host' that you've set your domains up with turns out to be a redirect to the webspace. (you cna check this by trying webmail on your plesk box - if that resolves, then all the other DNS entries will resolve too. If not.. then you've probably only got www.*
access). To fix this, you'll need a free DNS server somewhere where you can create an entry for a single domain (that is hosted on your plesk box). Once that's exists, you can then point all your other domains to use that 'master' domain's NS.
If you look on Plesk's DNS control, you'll see the dns entries it creates. Each one of those is hosted by the DNS server running on your Plesk box. All you need to do is get the rest of the world to see them.
I hope that makes sense, I had to retype it after refreshing my browser
For googling, search on DNS resolution, or look here: http://www.tcpipguide.com/free/t_DNS...ionProcess.htm