Which version of Zoiper are you using Is it Zoiper Classic or Zoiper3?
Zoiper 3.6.25251 32bit
This is not the Biz version
Zoiper 3 Free keeps the config files in the appdata folder for the current windows user.
Make sure zoiper is not running, then open a file browser, type %APPDATA% in the address bar then press Enter.
Copy the folder named Zoiper.
Paste that folder in the relevant destination on your new computer.