For starters and in general, she has the authority to use deadly force in certain circumstances with the ship's weapons. That's just one example.
She just can't go firing on any ship. They have to be a threat to her ship. Tuvix posed no threat.
Although the Doctor determined that his ethical subroutines could not allow him to perform the procedure, no one stepped forward that I recall and protested the action as being against Starfleet regulations. If Tuvix had, as he claimed, Tuvok's knowledge as security chief, I'd've expected him to put that forward as an argument in his favor, if Janeway were actually exceeding her authority. His appeal was primarily to the ethical issue of right and wrong. The episode provides no reason to assume that Janeway is exceeding her authority.
Janeway is 70,000 light years from home. She is the final authority. She would've never made the same decision in the Alpha Quadrant. So I'd say she didn't have the authority. She did it anyway. Like she violated other Starfleet regulations in the Delta Quadrant.
Tuvix, with all of Tuvok's knowledge of Janeway, likely knew appealing on regulations was a fool's errand.