A line in chapter 36 sums up Mig's reaction to the ill-conceived plan that the rat presented to her. "But Miggery Sow, as I pointed out to you before, was not the sharpest knife in the drawer."
This fact about Miggery's intelligence is stated time and time again, somewhat rudely, over the course of The Tale of Despereaux. When Roscuro tells Miggery his plan to make her the princess instead of Pea, the poor serving girl fails to see the obvious ridiculousness of his proposal. Sadly, at this point Mig doesn't see any flaws in the rat's plan, which he never clarifies is revenge until it is far too late. After the two of them have already taken Princess Pea into the dungeon, Roscuro orders Mig to chain up the princess. Mig argues that the princess is going have difficulty "learning her lessons" if she is chained up, but the rat is insistent that she obey him.
Mig's realization that the rat has no intention of honoring his promise to her comes far too late and the reader is left wondering how on earth she could have been so clueless. However, there are some very important reasons why Mig went along with such an idiotic scheme. It is stated very early on in Mig's story that her mother died when she was six and that she was sold as a slave by her father soon after. Mig, who was twelve when she met Roscuro, had been abused and treated with extreme cruelty nearly her whole life. Considering her tragic upbringing, her intelligence and understanding of the world was never properly allowed to develop. On top of that, the abuse she received was frequently delivered to her ears, meaning that there is every possibility that her head was hit on numerous occasions and she may have suffered brain damage.
In the end, though, perhaps the most likely reason that Miggery would so blindly follow a rat with such a lackluster plan is that she desperately wanted to be a princess and live a good life. Roscuro was one of the only people in her life to ever show her compassion or an ounce of respect (even though he was only pretending) and she trusted him instantly to give her the happy ending she so dearly craved.