Connecting My Book Live Duo directly to PC

Exactly.

Both devices are connected to 1Gbps Ethernet, that allows maximum speed for data transfer. you could still connect to your internet router via wifi, so the internet will be availible too, so the primary goal is achieved without configuring anything, just plug it in.

To increase comfort for all your network, you have to set up the WIFI mode of your new router next to the PC correctly. Set it to bridge and turn off the DHCP server. It should recieve the IP Adress from your internet router. You will have 2 wireless networks then, and no matter in which one you connect to, both internet and acces to MBL should be availible

If you do skip this step, your MBL will have no connection to the internet and only devices that connect to your new router can access the MBL, and only devices that connect to your internet router will have access to the internet. So that is also the way to test if you did the config right