Exchange mail from within .local domain with outside world

Hi all,
I created a private domain and use Exchange 2003.
Now I can send mail to my Gmail account just to test that Exchange is working properly.
I also receive it on my Gmail account.
However, I cannot reply to the received mail message.
When I do, an error returns stating `DNS error, domain name not found`.
As smart host, the ISP address is used.
How can I determine what caused this error?
I also have a public domain, how can I use it for DNS?