The information Dorium gave was about the Silence, and their phrase "silence will fall" (or, as he says, perhaps more properly translated as "silence must fall").
Dorium knew that the Silence were trying to stop this question being answered, due to a prophecy that Bad Things would happen if it were answered.
We now know, after, The Time of the Doctor, that the Bad Thing was the return of the Time Lords to the universe, and the resumption of the Time War.
We never find out how Dorium learned about the Silence's motivation. But I don't think it's particularly surprising for Dorium to know this, and for the Doctor (or the Teselecta's crew) to be unaware of it. There's no reason the Doctor would know about the Silence's motivations, and every reason he wouldn't - you forget having seen them as soon as you look away from them, and their entire purpose is somewhat anti-Doctor, so they'd probably be keen to hide it from him.
Speculating, Dorium is a black marketeer (we see him selling a coveted vortex manipulator to River), so he's likely to come into contact with a lot of shady people, and thus hear things. Beyond that, he told the Doctor about the question after he had been beheaded by the headless monks, who (I think?) are part of the Silence. He may have overheard this detail from inside his little wooden box.