Ice cream and other dairy products can cause dogs AND cats to have digestive problems. I doubt if a small amount of ice cream usually would, but it could.
Dairy Queen ice cream is barely dairy...
And sugar is bad for humans. I think it's clear that DQ is not a health food store for any species.
I work in the pet industry and ice cream and treats as such are designed for animal consumption. It's not the same as we eat...so put down the torches and pitch forks