The classic image of the cavalier is the chivalrous noble knight.
This is actually not accurate - your image is probably coming from the AD&D class. I think one of the underlying issues is how literally to take the name Cavalier, with the answer being "not very".
The classic Cavalier archetype would be an upper-class, cause-driven, court dandy/puffy shirt/swashbuckler type who was a mounted cavalryman and officer on the field of battle because of his station in life. Sword and shield doesn't suit them very well. A better non-mounted option would be to go the swashbuckler/dps route - off his horse a Cavalier would be a wealthy warrior-rouge type with fancy dress, a cavalier attitude (hint hint) and knee-deep in court politics. It would be interesting if this was the concept for the class, because it is more historically accurate and a rather unique concept when it comes to RPG classes.
However, the presented class is really more of a Knight archetype with the Cavalier title used loosely as a synonym (a la AD&D). They do touch on some more Cavalier-like ideas in the Order options and the description of being dedicated to a cause and their role outside of battle, but it's just lip service - those Cavalier-like ideas aren't reflected very well in the game mechanics of the class.
I think an unmounted heavily armored, sword-and-shield defender option is a good fit for a Knight. It also fills a niche and solves the only-good-on-a-mount problem, so ultimately I give the idea a thumbs up. If I had to make the final decision I would rename this class to Knight, add the sword-and-shield defender option and then save the more unique Cavalier archetype for a prestige class.