The easiest way to do this to to buy an external hard-drive as I've already done this!
Go into 'My Music' and drag the iTunes folder onto the external hard drive (this may take a while if like me, you have alot of music on it!)
Once it's on the hard drive, download the latest version of iTunes on the laptop and get the empty library open. Drag the itunes folder into it and again, this will take a while and this will automatically sort all your music. Once this is complete, go into the 'Advanced' tab and click 'consolidate' and this will copy everything into the empty folder in the music section of the new laptop and job done!
You don't need to re-register and you can just log into the new iTunes account as normal.