@Solipsist She was twelve and no matter how much game of thrones she might have watched in her past life, she is not a hyper competent master of palace intrigue. (like you normally end up with in these sorts of stories?)
It's actually better for her that she hasn't attempted any of your suggestions because the attempt would end up sloppy and amateurish which would in turn make the empress question her usefulness.
By not having a spy network, the Empress has probably been trying to wrack her brains trying to figure out how the hell she knows so much to no avail which greatly increases her perceived value as the queen's spy/lackey.
It's already impressive that she's roughly managed to play both sides against each other to forge a path of escape.