Umm that was a little confusing, but skybolt link is a good one to follow if you want to move your iTunes to be "shared" this can also be done by moving iTunes to the Public or User's/Shared folders for local net or across the net.
Before I start confusing you, you can without harm use Target Disk Mode I've done this three times now since 2003 moving my stuff to new computer without problems & at the time had no backup's!
Ofcourse with Leopard you've got Time Machine & has advised to back up your important files if you've got an extra HD? Getting back to those Folders in Music/iTunes you should see >Album Artwork, iTunes Music, Previous Library Folders plus your actual iTunes Library & XML file. Don't mess with those at all.
In my Previous Library I have 8 libraries altogether backdating to 03.
Still you can back up your iTunes from Panther to HD, but this will leave the Permissions of that iTunes Music
with the old Panther User & Password has "Author" this is OK if your going to use same U&P on new machine you don't have too.
Then follow this to allow others to share your iTunes Music Folder on the HD
http://support.apple.com/kb/HT1203 Don't be worried about the term "Publicly Accessible" that's just what your HD is once you setup correctly... even more so easily if you've got an Airport Extreme or TC connected to it.