Yes, you can transfer the profile (data+configuration+logs) from a host to another by using the web interface of Zeroshell.
There are to possibilities:
1) From the section [Setup][Profiles] select the profile you want to transfer and then press the button [Backup]. A compressed file will be downloaded on your web client PC. Using this you will have to restore the profile on the other CPU.
2) Plug an external USB disk and use the button [Copy] to make a copy of the selected profile on this disk. Notice, that in this case, the copy is not compressed and Zeroshell can directly use it as profile without restoring.