Kirk knows that the attackers of the Kelvin were Romulans despite the fact that nobody at this time has ever seen a Romulan, nobody on the Kelvin identified them as Romulans, and no one on the Narada said they were Romulans.
Reports of a Romulan attack in Klingon Space where one ship destroyed 47 ships is only news worthy to a room mate and not the entire federation. And even if she did report it to someone, the idea that one ship was able to destroy 47 Klingon Ships, a race known for being aggressive and fighting to the last man isn't worth concerning over with anyone? So let me get this straight.
47 Klingon Ships destroyed by one Romulan ship = No concern.
A vague distress call from Vulcan that could be weather related = ALERT EVERYONE! SCRAMBLE ALL JETS!
Looks like its feeding time, let me get my spoon.

Guy who looks like a Vulcan destroys a UFP ship. They have him on video and audio. Gee, I wonder if someone might be able to figure out they were speaking Romulan by comparing those recordings to recordings from the Romulan War? No doubt the Vulcans will have some 'splaining to do, though.
I'm sure someone in Starfleet Intel is working on the matter of the 47 Klingon ships, but that someone isn't on the Enterprise so it doesn't figure into the story.
Uhura isn't an engineer, a pilot, a scientist or a doctor. She's in communications and in th movie perform communications related duties. And in that function provides information that helps Kirk solve a particular "puzzle."