This Straits Times (9 October 2008) headline, though perfectly grammatical, amused me because I couldn’t get the idea out of my head that the writer meant he spotted a very young insect (e.g. baby fly vs adult fly). This interpretation has the noun phrase a toddler fly, with a as determiner, fly as head noun, and toddler as noun premodifier.
The intended meaning was, of course, that the writer saw a toddler go up in the air when turbulence hit the Singapore–Perth flight. Here, the noun phrase is a toddler, and fly is a non-finite verb.