You don't have to delete anything from the Asus. You can copy your iTunes library from the laptop to the Mac. Read this for more information.
I synced my ipad2 with an asus laptop. Now I have a Mac mini that I want to use for syncing and backup. But when I connected my ipad to the Mac mini it said something about the ipad being already synced to another computer and backup is permitted only one computer at a time. How can I transfer my backup to the Mac mini ? And delete my previous (I.e. asus laptop) iTunes backup system?