Would a slightly larger diameter pot work or does it need to be deeper?

Karley Rose is really one of the most suitable ornamental grasses for a container. And now is a good time to do some work with it :-) I'd remove it from the container, do some root pruning and then divide the current clump into several more but replant them all in the same container - with fresh potting soil - for a full, lush look. Next season you can do the same but start some in a second container as well.