Change of domain?

Hi guys.

I have set up a wordpress blog on my server here;
http://nibs.ryng.co.uk but have bought a separate domain name for it.
http://www.nibonsai.co.uk

At the minute nibonsai.co.uk is framed web-forwarding to nibs.ryng.co.uk, but what I ideally want is to keep hosting the blog at nibs.ryng.co.uk but change all the links to nibonsai.co.uk/ and have http://www.nibonsai.co.uk as the main domain.

I hope this makes sense. Any help would be much appreciated.