Here’s a list of all World of Warcraft: Wrath of the Lich King installers:
The download is 2.04Gb (on a Mac), I haven’t started the download on a Windows yet.
And yes, you will still need a beta invitation before being able to login!
As for the character copy, it was done within 10 minutes. Just 5 hours left on the download. 🙁
Edit: same size on a Windows – 2.04Gb. The download contains the setup.exe and the installer.app, so you should be able to copy it to any OS.