You need to copy the Domain.sties file that is located in your Users/Home/Library/Application Support/iWeb folder to the same folder on your new Mac using one of the methods Wyodor linked you to.
But remember that in Lion and Mountain Lion the Home/Library folder is now invisible. To make it permanently visible enter the following in the Terminal application window: chflags nohidden ~/Library and hit the Enter button - 10.7: Un-hide the User Library folder.
To open your domain file in Lion or Mountain Lion or to switch between multiple domain files Cyclosaurus has provided us with the following script that you can make into an Applescript application with Script Editor. Open Script Editor, copy and paste the script below into Script Editor's window and save as an application.
do shell script "/usr/bin/defaults write com.apple.iWeb iWebDefaultsDocumentPath -boolean no"
tell application "iWeb" to activate
You can download an already compiled version with this link: iWeb Switch Domain.
Just launch the application, find and select the domain file in your Home/Library/Application Support/iWeb folder that you want to open and it will open with iWeb. It modifies the iWeb preference file each time it's launched so one can switch between domain files.
WARNING: iWeb Switch Domain will overwrite an existing Domain.sites2 file if you select to create a new domain in the same folder. So rename your domain files once they've been created to something other than the default name.