I don't think there'll be a PS3 version, otherwise DQH wouldn't be PS4-only in the west.
You have your logic a little mixed up there. DQH is PS4 only in the West because the PS4 is selling well in the West. It's selling not nearly as well in Japan (no home console is), so it's likely that, at least in Japan, it will be on both PS3 and PS4 to make up for sales they wouldn't get from it being a PS4 exclusive. It doesn't push more PS4 systems in Japan that way, which is certainly problematic in the long run, but it sells more copies of the game to the market where it will sell the best by far to begin with.
Edit: To note, it isn't an uncommon move at this point for Japan releases that came out on PS3 or PS4 and PS3 in Japan to only come west on the PS4. They're slowly phasing out PS3 releases of Japanese games in the West as they're becoming less necessary to facilitate the success of releases overseas.