He cares. He's an extremely vain person where any kind of criticism leads to deflecting or attacking others. If Donald truly didn't care then he wouldn't respond to most of his critics like a petulant child on Twitter.
Scott Morrison doesn't do that, and that's an extremely good thing. I'm no fan of the guy, but it's cringe-worthy how some people are responding to him taking some time off. Everyone deserves some time to relax.