Dany's problem is that she doesn't know how to run a country and is getting frustrated by how difficult it is. This isn't that much of a mark against her, no one currently alive in the setting knows how to run a country. And, indeed, many institutions that are absolutely vital to good and fair governance simply haven't even been thought of at this point in time.
The Sons of the Harpy are a good example. Anyone from modern Earth would immediately see that the solution is to create a national investigative and law enforcement service that answers to the crown and empower them to investigate such crimes. It isn't all that difficult to infiltrate a subversive organization or flip one of its members.
But J. Edgar Hoover hasn't been born yet in the world Dany lives in and the concept of a national police force isn't something that's really come up yet, certainly not a professional one. She isn't sufficiently innovative to come up with the idea on her own.