A MUCH easier way is to:

1. Create the new domain if it does not alreay exist.
2. Click the project name in the tree and drag/drop to the new domain.

Answer -
Below are the steps to move the project to a new domain in QC 9.2. As always, it is a good idea to back up before making changes.
* Create the 2nd domain in the Site Administrator - Site Projects tab
* In Site Projects tab, right click on project looking to move (in old domain) and choose remove project (!!do not delete project!!). Removing project just removes it's reference in Quality Center. Deleting the project will delete the repository and database for the project as well and no data will remain.
* open the repository in windows explorer and copy the project folder from the old domain folder to the new domain folder
(Program FilesMercuryQuality Centerrepositoryqc\)
* edit dbid.xml inside of the project folder in the new domain, change the tag to the correct path in the file system for the new domain
* In Site Administrator - Site Projects tab right click on the new domain and choose restore project
* Browse to the corrected dbid.xml file in the new domain's folder in the file system
* In the Site Administrator - Site Projects tab, right click on the newly created project in the new domain - activate project