Use different DNS servers for guest network on AirPort Extreme/Express
What you are suggesting will provide name resolution to the 192.168.1 subnet but has nothing to do with restricting access. 

The correct way to do what you want is to firewall the device, or have no routing between your subnets. 

If you do want to set up just the DNS settings then all you have to do is propagate them via DHCP. This means having two separate DHCP scopes, one with the google DNS servers, and one with your internal DNS server.