My thinking on this is as follows. Whispering in regular languages isn't usually semantically or phonemically salient. It's almost always just a modulation of speech in compensation for the physical or social environment. For this reason it's not transcribed in phonetic notation, just like shouting is usually not transcribed.
Sometimes whispering can be phonetically salient, though. This is rarely if ever the case as part of a language's sound system, so there hasn't been any need to notate it much.
Now, whispering is definitely phonetically salient is in the study of speech disorders. Dysphonation of various types is found among those with disordered speech. This includes inappropriate whispered, creaky, faucalized, unvoiced, mouthed, etc. phonations, ingressive airstreams, etc. Fascinatingly, though the Extensions to the IPA[PDF] do not actually include a mechanism for indicating whispered phonation! Wikipedia says they do, but it's not clear to me that this is actually true.
The IPA does include a variety of diacritics for phonation types, but whisper is not included.