She has every reason to want to get rid of Robert, since Ned has told her that he knows that young Joffrey is not Robert's son. And she makes a move to have Joffrey immediately become King, right after Robert dies.
Ned is ready for this. He has the King's dying instruction in hand - appointing Ned the realm's protector, until the "rightful" heir takes the throne. The "rightful" is actually Ned's word, which he gets by the dying King, who wanted Joffrey's name in his last proclamation. Ned is not above deceit, either, if it's for a just cause (or, a cause that he deems just).
But Ned is not ready for the double-cross of Little Finger, who turns his men on Ned, right after Ned turns the tables on the Queen. One of the best things about this Game of Thrones is how just about any piece on the board can suddenly swivel around and attack a presumed ally.
Meanwhile, although Ned did manage to countermand the King's order to kill Daenerys, it's not in time to stop the assassin, who tries and fails to poison Daenerys, thanks to Mormont's sharp intervention. But the attempt enrages Drogo, who now vows to the cross the "poison" sea and claim the "iron chair" for Daenerys.
When you add word from the north that the strange creatures were not gone, only sleeping, now awake, and Daenerys's increasing interest in dragons, we have some good moves and fierce battles ahead in Game of Thrones.
See also A Game of Thrones: My 1996 Review of the First Novel ... Game of Thrones Begins Greatly on HBO ... Game of Thrones 1.2: Prince, Wolf, Bastard, Dwarf ... Games of Thrones 1.3: Genuine Demons ... Game of Thrones 1.4: Broken Things ... Game of Thrones 1.5: Ned Under Seige ... Game of Thrones 1.6: Molten Ever After
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