You do not copy, you install. So, in other words, you need to copy the installer files to your Mac mini, not the already installed program. Activations can be manged from the Help menu and you have two of them. So until you are up and running on your new Mac, there is no urgent need to deactivate on the old Mac.
I actaully copied over the insaller files to my Macmini before I installed Illustrator CS5 on my old iMac.
Now from my Macmini, I tried to install CS5 and it tried to do it, but I got an error - "Your installation encountered errors" Please try and restart your system and try again. Installer failed to initalize. I restarted but got the same result. I went to the Adobe Application manger in the Help menu and got this messgage - "Help isn't available for Adobe Aplication Manager." What can I try to fix this and get Illustrator CS5 installed on my new macmini. This is an upgrade to CS5 from CS2.