Safari SSH Tunneling Troubleshooting Diagnostics
The reason your attempt fails is because the remote host (i.e. the router at mydomain.fqdn.com) doesn't allow you to forward the traffic through the SOCKS proxy. This is the meaning of the "open failed: administratively prohibited" message.

In order to fix this, you'll need to change the SSH configuration on the remote router at mydomain.fqdn.com. In case that system uses OpenSSH, you need to check that your sshd_config adheres to the following:


AllowTCPForwarding must not be set to "no" (i.e. don't set it or set it to "yes")
PermitOpen must either not be set, set to "any" or set to allow the IP address of the "www.whatismyip.com" web site you're testing with.


If you're using SSH keys to authenticate, check that your authorized_keys file on the router does not have a "no-port-forwarding" limitation on your key, or that you have "permitopen" limitations that doesn't explicitly allow the IP address of the "www.whatismyip.com" web site. 

If the remote router uses something else than OpenSSH to offer its SSH service, it might not support the TCP forwarding / SOCKS proxy feature at all. You'll want to check the documentation for the device to see if it does support the feature, and if so, how to enable it.

UPDATE: You have updated your question to include information that indicates that you're using a "homespun" router using a variant of OpenWrt. In addition you specify that you have just the openssh-sftp-server package installed.

The solution is then to install the full OpenSSH, namely from the openssh-server package. You can do that with the following command on the router command line:

ipkg install openssh-server