As Florian said (and based on what I've just tested), doing either "Select text -> Middle click to copy -> Middle click in another window to paste" or "Ctrl-C and Ctrl-V" copies the http:// over, *even when http:// isn't visible in the omnibox (the edit field)*. I'm not sure if there is a configuration problem on your system or if it's something specific to the DE (I'm on KDE).
As Florian said (and based on what I've just tested), doing either "Select text -> Middle click to copy -> Middle click in another window to paste" or "Ctrl-C and Ctrl-V" copies the http:// over, *even when http:// isn't visible in the omnibox (the edit field)*. I'm not sure if there is a configuration problem on your system or if it's something specific to the DE (I'm on KDE).