It's pretty easy to move the content and the primary entrance to your site to domain2. One thing you need to consider is if you have made 'absolute' links within your site that point to domain1. In a perfect world when linking within your own site you would always use 'relative' links for things link images and links within the site.
The general steps are:
1 - add domain2 as a fully hosted domain via manage domains. IMPORTANT: configure it with the SAME user as domain1
2 - if the user does not have shell access, upgrade the user by editing the user on the Manage Users page.
3 - if this is worpresss, login to the WP admin and change the domain in the settings, you will get an error and your blog will not be available until you have completed the next step.
4 - login to your users shell account and swap the files for domain1 and 2...ie:
mv domain2.com to temp-holder
mv domain1.com domain2.com
mv temp-holder domain2.com
5 - once you are sure you don't want to reverse this process, you can remove hosting from domain1 and add your redirect or mirror.
Note if you are using wordpress step 3 must precede step 4. If your not familiar with these steps you may want to enlist the help of a friend that has basic linux/unix knowledge to help. since every situation is a little bit different it's only possible to give the general steps.