So long as your modem IP is different from the Linksys router IP you're ok.
Normally the DNS servers are from your ISP or you can use OpenDNS if you enter it in the router, as well as TCP network properties.
If you use a chain of routers (as might be the case here), the routers can be set as DNS servers, one to another, then out it goes to QUEST.
Your modem's internet address is one thing. That's what you got from QUEST.
Then the modem has its own IP address, assuming the modem does NAT=network address translation.
Then, if you set it up correctly, the modem gives out the address to the WRT54GS, which from your computer looks like internet address.
Then, if you use the Linksys DHCP service, the Linksys router gives out IP to your computers.
And in ipconfig /all you'll see DHCP and DNS snd gateway all having the WRT54GS LAN address.
That said, I don't think I really understand your question
What do you mean by "dynamic DNS"?