In British English we would almost certainly say "I haven't brought it." Because as it is important, it must be relevant to the present situation. The (lack of a) past action is connected to the present.
We would probably say "I didn't bring [something]." if we weren't expected to bring it, as we wouldn't really be connecting the past to the present.
But I agree with fdmaxey that in this case, the difference is small.