Don't sync it to an empty iTunes library. iTunes syncing generally works one way, from computer to iPod. Syncing an empty iTunes library makes the iPod's library empty.
You cannot use iTunes to transfer song files from iPod to computer, except for songs purchased from the iTunes Store. However, there are third-party methods and utilities that can transfer from iPod to computer. If you do an Internet search on something like "ipod transfer," you should get some links. (The CNET article seems to be popular.)
Once the song files are on the computer, you can add them to your new iTunes library. Then, (after confirming everything is there) re-sync your iPod to your new iTunes library.