It sounds like you dont want your child accessing websites. You can't remove all browsers, since Windows Explorer is a required Windows program, but is also usable for web access.
You should be asking the question "is there a way for me to disable internet browsing on a different user name, but still allow him/her to use Outlook?"
Unfortunetly I don't know how to do that specifically, but it's very easy to disable the internet all together. Also, would you want your child to have access to IM programs like AIM, MSN, or Yahoo, or strictly just Outlook?