Is this Croatia plan feasible?

It sounds like the best route, the ferries are fine. And yes it is okay to book online. Since the Croatian coast is becoming so very popular, i would rather have my reservations and not have to worry about getting there too early to secure a seat.

You may not find much accommodation on Korcula for just one night.

On the mainland, Omis or Makarska would be good half way points en route to Dubrovnik.

I traveled in the opposite direction a few years ago: Dubrovnik - Korcula - Split. Back then, there was no ferry option (in October, anyway) between Dubrovnik and Korcula, so I took the bus. I think going the opposite direction, the bus would leave Korcula Town at the crack of dawn, though, which makes spending just a night in Korcula kind of a stretch and maybe not worth the hassle. You might consider just doing a day trip from Split to an island like Hvar by catamaran and stay in Split an extra night, then just take a direct bus from Split to Dubrovnik.

I wouldn't split up the bus trip between Split and Dubrovnik myself - just get it over with. Make sure the bus is as direct as possible. I get motion sick on some buses, too, and can't do anything on a bus except look out the window. I spent a night once (not while traveling by bus) in the town of Baska Voda, in the Makarska region. It was an OK little town but otherwise forgettable. I think an extra night in Split with a day trip elsewhere (e.g. an island) would make more sense.

If you want a significant bus stop in between Split and Dubrovnik, Mostar would be my choice. You could do that by bus - but of course, that means even more time on buses, because you must detour inland to get to Mostar. It would also be possible to rent a car for two days and just drive from Split to Dubrovnik and stop in between (e.g. in Mostar). I much prefer driving to being a passenger - I don't get motion sickness when I drive. It might be kind of busy to drive on the Dalmatian Coast in August, though - maybe a lot of traffic.