I haven't heard a hiccup, but I have seen what I think is a hiccup. Muffin sometimes sits there and her body moves periodically like she's hiccuping.
To be totally honest, rabbits can vomit. It's extremely rare, so we usually just say they can't. Hiccups also don't come from the stomach but from the lungs and are similar to the way the first land animals breathed--like a lung fish, the body had spasms that opened air-filled sacs (lungs) where gases could go into the blood. These spasms remain in more evolved organisms like humans as a vestige of our ancestry to the first land-dwelling, air-breathing creatures. Pretty much everything that lives on land can hiccup.