Hello, I just deleted a few lines. I'm sure there is a better way but this works for me. Also, I set the IP address to be the subject of the email as well as the text in the body.
Cheers! - JP

set response to do shell script "/usr/bin/curl http://checkip.dyndns.org/"
set ip_address to extract_ip(response)
set mailto_addr to "YourEmailAddress"
send_ipget_mail_message(mailto_addr, ip_address)

on send_ipget_mail_message(email_address, ip_address)
tell application "Mail"
activate
set composedMessage to (a reference to (make new outgoing message ¬
at the beginning of outgoing messages))
tell composedMessage
make new to recipient at beginning of to recipients ¬
with properties {address:email_address}
set the subject to ip_address
set the content to ip_address
end tell
send composedMessage
end tell
end send_ipget_mail_message

-- Function to extract ip from HTML returned by dydns.com
on extract_ip(this_text)
set clean_ip to ""
set this_char to ""
repeat with this_char in this_text
set this_char to the contents of this_char
if the this_char is in {"0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "."} then
set the clean_ip to the clean_ip & this_char as string
end if
end repeat
return the clean_ip
end extract_ip