Hey Mark,
There isn't a report that displays this (but that's a great idea and one I'll pass on). To do keyword research on your Shopify site, the simplest way to do that would be to use Google Analytics. CrazyEgg has written a really great guide to setting up parameters to do that.
Shopify's built in search will look like this: yourstore.com/search?q=search+term
Hopefully this helps!