Hello! Usually it is enough just to move the folder. But check Paths section in WinUAE config - they should all point to AmiKit folder except the Configurations which should point to AmiKit\WinUAE\Configurations. Or you might want to click "Reset to defaults" button there.
If it doesn't help, here's another approach. Install fresh new AmiKit on your new computer (without installing AmigaOS) and then just copy AmiKit\AmiKit\AmiKit.hdf file from your old computer to your new computer. That file includes all of your Amiga files.
Hope it helps?