nathanvit,
I do not like this one bit - you really need to consider what could go wrong and try to develop a solution with that stuff in mind. For instance - is the reason the router changes it's IP everyday for security? If yes, you are now sending the IP in an email over the Internet. Only you will know the things that could go wrong, so I won't get up on a soapbox.
Create an alias that pipes the email to a script getip : "| /usr/local/bin/get_ip.pl"
In the get_ip.pl script, have it ping your broadcast 192.168.0.255 for instance
Have the script then perform an arp -a
You will have to hardcode the MAC address of the router so it will know what to look for - use a regex to extract the IP address
Finally, have the script send the IP to your home address system("echo $ip | mailx -s "today's IP" youraccount\@nowhere.com");