Gaye, in theory the answer is yes. The word is in our list, and in fact is labelled as common. However it is not one of our 9-letter "seed" words, which means it would never be used to create a puzzle. And since there is no other 9-letter word using the same letters, "whodunnit" will never come up in a Chihuahua puzzle.
I think the spelling "whodunit", with one N, is a bit more widely used. Was that one of the words in the solution?
When I was designing the game, I concluded that some of the 9-letter words I had labelled as common were not quite common enough to be used to generate a puzzle. I've previously had a bit of a whinge about some of the unusual words popping up as the 9-letter word in The Age.
(You may ask why the word list includes words that can never be used. Well, apart from the fact that it could be easier to leave them in than to weed them out, it also means the list is suitable for use in other word games that I might get around to creating one day.)