There are several people on here who do get awakened in the middle of the night with diarrhea, although I think maybe you get up more than anyone else; I think most IBSers are worse in the morning because as soon as they eat, they get everything cranked up. But no, it's not impossible to have IBS and to have it wake you up in the middle of the night.
I think it's more common for people with bad gall bladders to get awakened during the night, but they always have other symptoms, like a lot of pain, some nausea or even vomiting, and a lot of bile in their diarrhea (yellow and burning). If you don't have any of those problems, then yes, it's probably just IBS-D. I'm guessing your doctor has already ruled out IBD? That usually has a lot of other symptoms too.
Have you tried changing when you eat supper and what you eat for supper? That seems to be the meal that sets you off. Maybe you can eat a medium-sized meal in the afternoon and then just have a little snack an hour or so before bed if you are hungry. Maybe that will help your guts settle down before you settle down for the night. You might also want to keep a diary of everything you eat and what kind of reaction you have; a lot of people have discovered things they can't eat that way. Apples and apple juice are almost universally a no-no for IBSers, as are all forms of sugar alcohol (found in low-sugar and sugar-free products). Caffeine and alcohol also bother a lot of us who are prone to D. A lot of people also have problems with dairy, but then some, like me, don't; you just have to try eliminating it and see if it helps any.
If you have diarrhea, you can also try taking a Caltrate 600 w/vitamin D supplement pill or two before dinner. The calcium in that brand has a constipating effect--it absorbs excess water. A lot of us have gotten some or even total relief from diarrhea by just using it.