Sure.
I am not totally sure where you are setting up the DNS, buy in most HOME networks, 192.168.1.1 refers to your network's router.
So if an application asks for your Domain Name Server address, you can use 192.168.1.1 and router will fetch the IP address....
IF the router resides on that address, AND there are DNS server entries set up in the router.
The router will assign IP addresses for your devices via DHCP and route internet traffic to them. It will use standard internet traffic port unless you tell it different.
Many people may have Incorrectly configured DNS entries in their router for their ISP's DNS servers,
or the ISP DNS servers are not as robust or updated as Google's PUBLIC DNS servers.
So using Google Public DNS servers 8.8.8.8 or / and 8.8.4.4 can sometimes speed up internet traffic, failures to connect name resolution etc.
I don't explain this as clearly as Google does...
Check this page for a thorough run down
Get Started | Public DNS | Google Developers