A connection reset indicates that the device you're connecting to has refused the connection. This can be a case of a port not being permitted through a firewall or it could be as simple as there being no DNS running at the other end.
Are you trying to actually connect to the router for DNS resolution or are you trying to connect to an external DNS server through the router?
If it's on the router, make sure that you have "ip dns server" configured or there will be no DNS running. You can verify that the ports are open by using the "show control-plane host open-ports" command and looking for the DNS ports (53/tcp and 53/udp) to be in listening state.
The output should look like this:
edge#show control-plane host open-ports | include :53
tcp *:53 *:0 DNS Server LISTEN
udp *:53 *:0 DNS Server LISTEN