Hi Phil,
Here is what I would do:
1 - You said you have a "different domain" - So set it up (DNS) to point to the same server;
2 - Use your control panel or IIS directly (not sure what you have there) to setup a new site on the server pointing to the new domain;
3 - Install the latest DNN version;
4 - Build the site up;
5 - Once the site is done, you could potentially just repoint things over on IIS (don't forget to create the new site alias on the new site pointing to studentcoaching.co.uk) - Or if you use a control panel, you could copy the new site on top of the old site.
I have oversimplifies things here so this can become short, but as you go along, if you have any additional question, just ask.
Cheers,
Aderson