She is literally the prime minister, the leader of the ruling party/coalition. Pass a legislation mandating equal pay with strict enforcement mechanisms if she actually cares about it instead of striking.
What’s next, CEOs doing solidarity strikes for worker safety instead of making the workplace safer?
It's based on the living tree doctrine, which was included in the Canadian Charter of Rights and Freedoms by the PM who created that, initially, by declaration.
Yes, if she cares about it strongly enough. Iceland is a parliamentary democracy instead of a presidential democracy - it means that the PM is the head of the government, the head of her party, a legislator, and the head of the coalition at the same time. She can force the issue. The only way to stop her would be for the other coalition parties to go against her, dissolving the government itself.
Of course, there is no need to stop her as she isn’t using her power that has been vested in her by the people to exercise on their behalf. She’s on a strike instead, a strike against herself essentially since she’s the only one who can do anything about it.