How to transfer music betwen Mac's?
If you have all the files in your iTunes library, then simply copy the library folder from its old location to ~/Music (the Music folder in your home folder) on your new account. Launch iTunes and it will detect the library.

If you wish to have your library elsewhere, place it somewhere else, then hold ⌥ as iTunes launches for the first time to let you select the library location.

With regard to the actual copying of the files, there are a number of ways you can do it. The easiest way may be to copy it over the network — AirDrop or AFP will let you copy the library, albeit pretty slowly. Alternatively, if you have an external drive big enough, you could copy it to that, then move it off onto the new Mac.