To create a keyboard short-cut that inserts the date and/or time in a Word document, you'll need to create a macro (that's because the Alt+Date creates a non-static field which means the date will change to the current date each time you open the document).
I like what this commenter suggested, and it's exactly what I did:
"I just created a macro (Insert Tab->Date and Time->format I wanted and made sure the Update automatically box was unchecked. I assigned it to ALT-D and it works fine."
Source: Different Ways of Inserting Dates (Microsoft Word), and in the comments section see Graham Hyman's comment