There is no merge option for projects in Site Admin. This is not a feature provided by the product.
Why do you want to merge projects? What sort of data are you trying to merge (requirements, tests, results...)?
You could, potentially, write a program using the OTA API to extract data from one project and insert it into another. The tricky part would be maintaining all the cross references, which would have to be reset as the records all got new absolute IDs.
The Open Test Architecture Application Programming Interface (OTA API) comes with the product. Documentation for it is in the Documentation Library accessed through the Help menu.
Basically, you write your own program to use the available interfaces in the OTA API. Depending on how much data you have this could become quite complex.
Some of the data can be moved manually. Open two browser windows and log into the two projects. In the smaller project go to the Requirements module and select a top level folder (not the root folder, but one that is directly below that). Right-click on it and select Copy. Then go to the window where the other project is displayed. Go to the Requirements module there. Right-Click on the root folder there and select Paste. Everything in the folder you selected should be added to the project. However, I don't know to what extent things like links to test cases can be maintained in this manner. And this process doesn't work at all for test results (Runs).
All of this could be managed with the features in the OTA API, but you have to look at a lot of things, like customized workflow, user defined fields, and customized lists, plus attachments, links between records, and so on.
Depending on what version and edition of QC you have, there may be other options. In newer QC products there is a thing called a Baseline, where you can "save" a set of data. If you have a high enough edition (i.e. Premiere vs. Starter) you can also share these baselines between projects. That might be another way to move the data.
Alternately, you could contact HP support. They might have other methods for merging projects that are not readily apparent.
It may make more sense to merge your reports not your actual projects. I'd be inclinded to wait until the next release to merge the projects.
For one project all their ids are going to change. You might want to make sure that your users are aware of the implications of the change. Often defect ids are referenced by developer tools and changing them has the potential to break all those references if the change is not managed in both QC and the developer tools.