I'm no iTunes expert, and you may want to wait for others to chip in, but when I've done what your trying to do in the past, this worked for me.
With the two Macs on the same network, from the old Mac copy the iTunes folder within the Music folder across to the Public folder on the new Mac.
On the new Mac, in the Music folder, if there is an iTunes folder, move it to Trash. Drag the iTunes folder you copied to the Public folder to the Music folder. Launch iTunes and it should find your music. If not, relaunch iTunes holding down the 'option' key and you'll be offered a 'choose library' window. Select iTunes in the Music folder and you should be good to go.