iPod Touch 4th Gen iOS 6 update
Yes, Apple is still signing iOS 6.1.3 for the iPod Touch 4th Gen. So you should be able to upgrade to it through iTunes when it prompts you to update it.

Or you can also manually update it through iTunes:


Download the iOS 6.1.3 firmware (from the above link)
Connect the iPod to the Mac and run iTunes
Go to the device screen
Press Option and click the Update button to open a File Browser window
Choose the IPSW file you downloaded