Why is Dors able to act in this scene?

Question

In Forward the Foundation, there is a pivotal scene involving Dors:

When discovering that Tamwile Elar has been secretly plotting against Seldon with the help of the military junta, Dors is seemingly overpowered by a device created by him which reveals her nature as a robot. Unbeknownst to Elar, though, she is able to use the last of her forces to overcome and strike him to death. The point is that by doing this, she breaks the laws of robotics.

My question is why is she able to act upon this in the first place, given the implications?

Answer 1

Dors Venabili is a robot that manages to violate the First Law. She has some association with a well known Zeroth Law robot R. Daneel Olivaw.

R. Olivaw was the first robot to hypothesise the Zeroth Law, doing so in a conversation with his human partner (as a detective) Elijah Bailey on Bailey's death-bed. Olivaw told other robots about this law and the first instance of it being used in the canon is by another robot R. Giskard Reventlov, using it to prevent the destruction of earth and also breaking the First Law in so doing by killing telepathically the person trying to destroy earth.

Giskard passes his telepathic abilities on to Olivaw and, as we see in the later Foundation books, Olivaw is alive and well, using his abilities to further humanity and shape the destiny of mankind. It can be assumed that Olivaw used his telepathic ability to shape the robots, particularly Venabili, to further his use of Hari Seldon to create the laws of psychohistory and establish the Foundations.

Answer 2

To further support the idea proposed by bob1, that Daneel has somehow 'imparted' the power of (or obedience to) the Zeroth Law to Dors, we have the following conversation between the two robots and Hari, in Chapter 61 of "Prelude to Foundation" (in the "Heatsink" section), shortly after their arrival at Jirad Tisalver's house in Dahl (bolding mine):

"I understand," said Hummin. "Your efforts at learning brought you to Upperside in Streeling and to the Elders’ aerie in Mycogen and to who can guess where in Dahl. As for you, Dr. Venabili, I know you’ve been trying to take care of Seldon, but you must try harder. Get it fixed in your head that he is the most important person on Trantor — or in the Galaxy, for that matter — and that he must be kept secure at any cost."

"I will continue to do my best," said Dors stiffly.