You can use Outlook or any other email client with Google Apps.
First, you'll need to follow these steps to set up your Google Apps account:
http://en.support.wordpress.com/domain-mapping/add-email/
Then, you can configure Outlook by following this documentation which is on the Google Apps site:
http://support.google.com/mail/bin/answer.py?hl=en&answer=77689
I understand that you want to provide people with an @daniellaalpher.com email address -- this is possible with Google Apps.