To transfer the music, copy all the music files from the iTunes media folder onto a hard drive or flash drive, then copy them into the iTunes media folder on the new laptop.
Your iTunes music might not download automatically but if you sign into your iTunes account on the new computer, go into iTunes store then click "purchased" in quick links and follow the instructions from there.
OK I have done this recently and I found the answer by googling it......remember to import your new library.xml file to the new laptop as well!
Here is how you keep that precious library data eg playlists, ratings etc....
On your old laptop open iTunes - File - Library - Export Library and save the Library.xml file to somewhere you can easily transfer to your new laptop (eg a hard drive).
Then copy your music to your new location.
Open iTunes on your new laptop - Edit - Preferences - Advanced - Change Location
Enter the path to the new location of your files.
OK now here's the part I am confused about.....I think you de-select the keep iTunes organised and de-select copy music to iTunes options in the Advanced tab before closing it.
You will not see the music listed in iTunes yet, don't worry, we're getting to that next.
Go to to File - Library - Import Library and import the Library.xml file you exported from your old laptop.
Your new music files should then appear in iTunes with their info (ratings, play counts, playlists etc) still intact.
Then you can change the advanced settings back to whatever you like.
A side note and a Word of warnning - disaster resulted for me when I let the newest versison iTunes reorganise my files according to iTunes preferences - half the music had broken links after that including ones in my many playlists Boo hoo