Who did you register the domain with?
Whoever it is will usually support email forwarding, in exactly the way you are looking to use it.
i.e. you give out your email [email protected], that will then get forwarded to your normal ISP email, [email protected].
All that's then left to do is change your reply address in outlook, or whichever email client you use to be you new [email protected] address.
Try the web site of the domain registrar that you purchased from. I used Easily click here , and email forwarding was easy to setup.