There is no desktop mode anymore for the ipod touch, that's why the icon is missing.
The ipod should show up in the device list in iTunes, ready to sync.
Verify your system requirements:
Mac system requirements (copied from
http://support.apple.com/specs/#ipodtouch )
Mac computer with USB 2.0 port
Mac OS X v10.4.10 or later
iTunes 8 or later (9.2 for running iOS4)
But remember that your ipod will be erased during the first sync. To save your data, back up manually:
Make sure your Mac is authorized in iTunes. Disable autosync in itunes, connect your ipod, right click on it in the device list and choose backup.
This will save data, pictures and settings to itunes. See what's included in this backup here:
http://support.apple.com/kb/HT1766
Transfer your purchases the same way to copy all apps and bought media from the Store to your computer.
Set up at least one contact and event on your computer to be able the merge your calendars and contacts after your ipod got wiped during the first sync.
The rest of the data can be restored from the backup you made.
Restoring:
http://support.apple.com/kb/HT1414