Hi Matt,
The steps to migrate from one DB and QC server to a different DB and server would generally be as follows (the only issue may be when going from the older DB version to the newer, your DB should handle that setup and movement):

Disclaimer
While this example may meet the needs of your organization, the sole responsibility for modification and maintenance of the tasks is yours and NOT that of the Support Organization.
The intent of the information provided here is for educational purposes only.
As such, the topics in this document are guidelines only, and NOT a comprehensive solution, as your own environment will be different.
The appropriate system technical resources for your enterprise should perform all customization activities.
Best Practice dictates NO direct changes to any production environment. It is imperative to perform and validate ALL modifications in a test environment. Use the results and knowledge garnered from the test environment experience to create a customized Production Deployment Plan for your environment.

Older QC Server; Preparing Project for Upgrade
1. Make sure all objects are checked in for the Project if version control is being used
2. Deactivate Project in Site Admin
3. Disable Versioning
4. Verify Project
5. If necessary Repair the project either manually or with the repair tool. The verify project report will specify what can be repaired with ''Repair Project'' and what needs to be repaired manually.
6. Make a note of the ''Project Directory'' example, C:Program FilesHPQuality CenterrepositoryqcDomainProject

Transfer Project To New QC Server
1. Have the DBA copy the Project schema from Old QC Database to need QC Database
2. Copy the Project File Repository noted from step 5 above to the new QC Server file repository. The
default location should be something like C:ProgramDataHPALMrepositoryqcDomain

Finishing the Process on the migrated to server:
1. Open dbid.xml file in the project folder with a text editor like notepad or notepad++
2. Change , ,
, values to reflect the ALM 11 Environment. For the
value opening a dbid.xml for another project will give you this value.
3. Open QC Site Admin
4. Click Restore Project
5. Point to the dbid.xml file location (the one that was just edited).
6. Select which Domain to restore into.
7. Click Restore
8. Click OK
9. Click Close
10. The Project should now be listed in the Site Projects Tree in Site admin
11. Verify the Project
12. Repair Project if necessary
13. Upgrade Project if moving from an older version to a newer version
14. Repeat steps 11 and 12 as needed
15. Activate Project*

*Notes
After the upgrade, although the QC server may report the upgrade as complete, there is still a background process running to transform the file repository if an upgrade was performed (from one version to another). While the project is still usable, during this process, you will not be able to back up the project until this process finishes.

I hope this helps.