Can you propagate custom data in New Activity?
If I'm reading the code correctly, it sends the slightly misnamed "Cases - Send Copy of an Activity" template, found under Mailings menu > Message Templates, "System Workflow Messages" tab.

If you add a Smarty debug tab, like this: {debug} to the top of the template, you should be able to send yourself a message and see a list of all available variables, which you can add as Smarty tags.  If what you're looking for isn't there (I suspect it's not), you can add it.  The core code is here: CRM/Activity/Form/Activity.php.  You'd be better off using an extension that adds them as part of hook_buildForm though.