Holy balls, this must be it! I can remember that for years after I played the demo, I knew the name of the game, so I was quite certain that I would recognize the name the minute I saw it, and your post immediately hit my square in the face. Also, because I wasn't positive about it, I was afraid to mention that the name of the game started with, or contained, a 'Q'.
Apart from that I quickly recognized the player character. For some reason though, I thought he had purple clothing, but I must have confused that with the game's logo/cover. I don't know where the circus/themepark thing fits in, whether that was somehow connected with the demo level, or my mind warping the memory after so many years.
Thank you very much!! I was honestly intent on (internet)digging up old gaming magazines to look for this game, or to gradually work myself through all adventure games that had dos releases.