Hello Ann,
Thank you for your message.
No need to re-install Remote Utilities. Simply add your new license key to the License Key Storage as described in
this registration guide.
Before adding the new license key (the PRO one) please make sure to select the previous key (MINI) in "Available keys" list and then click
Remove selected key - this way you'll be able to add the new one to the keys storage.
Hope that helps.