It is merely a suggestion, but it seems by the true answer, as in ep252 in Konan's death episode that she went back to the Rain Village.
The reason for that I believe is for the fact that she wanted to continue save the Rain Village and control it as she did with Pain, it was their home after all. The flashback after the the previous screenshot scene kinda showing it.
As for the Tsuki No Me project, a careful examination of Pain an Naruto talk make it clear that the Tsuki No Me project was Pain's secret and true object for the Akatsuki that he hidden from the rest, as Pain telling Naruto they are going to control the nations through fear of Bijou's weapon. He also says that in one of the Akatsuki meetings. Seeing him so sure in that plan making us clearly see that Tobi hasn't shared the project with the rest.
Considering the above assumption, Konan clearly couldn't help Naruto in any of Tobi's Tsuki No Me project. And rather, thought the fact that not helping the Akatsuki anymore would be much help with the plan they assumed to be. And furthermore as I said she wanted to get back to the Rain Village and govern it as she always did.