I wouldn't recommend the h4n anymore. It is still a huge step up from the on-board audio, but it generally isn't the best value anymore. The H5n or H6n are both better options available now and generally better value unless you are getting a used H4n that someone is selling so they can buy the 5n or 6n.
That said, yes, you want an external audio recorder. The "internal audio recorder" on your camera is nothing more than a consumer level audio jack with a minimal quality capture capability. It lacks key features like phantom power and balanced audio as well as lacking a high quality audio interface. Monitoring is limited, the audio is heavily compressed and the connection is not secure and has to be plugged in to your camera.
An external recorder, such as something in the Zoom H#n series or higher end devices with similar function provides much cleaner audio as well as the ability to work with a much wider variety of high quality microphones. Additionally, you can still use the output from the external recorder and feed it in to your mic input on the DSLR if you want to have audio on your rough footage (though I still recommend using the actual audio files from the recorder for your final audio.) You don't need to have it connected to your camera if your camera needs to be moving. It can be operated by a separate sound engineer without bothering the camera operator. It is just all around a smoother and much higher quality experience.