This should work okay - do you get any extra error information when the test fails that will give a clue as to the problem?
You mentioned it sends to your email address okay, so the most likely cause is that you need to enter your credentials. Under the server name you'll see "Mail Server requires a user name and password". If you fill those in, does it work?
The reason for this is sending to an email address within your own organisation won't require any authentication (otherwise no one outside your company could send you mail). To send to an external address though (such as att.net) it'll need some form of security - this is to avoid your server being used for spam relaying.
The reason Outlook works fine is because it's pre-authenticated with Exchange. SQL Monitor connects using SMTP instead which doesn't work in the same way.