Hi @rkyat 
Welcome to the Community and thank you for the question.
As it stands, our Shotgun Support team is able to do a complete site copy from one site to another, but we can’t break it down into parts, such as an individual project copy.
The full site copy will overwrite any existing data/media/settings/preferences on the “receiving” site.
If you want a single Project copied over, you would have to manually recreate the Project template on the new site. Once that Project is recreated, you can export data from the old Project/site and import it into the new Project/site.
- Take also a look at this thread where it explains more about that
Export project templates to a different SG site?
Hope it helps,
Cheers!