Janeway does have the authority to order Tuvok to his death but doesn't have the authority to do so with Neelix. I'm not so sure whether she had the legal authority to order Tuvix to his death.
Even if she had the authority to (which I won't argue), that doesn't mean it was the moral thing to do. Also, under the Starfleet charter to seek out new life, even if she had the legal authority to execute Tuvix, that doesn't mean it was very principled to kill a new form of life or species.
Of course she has the authority to do whatever with Neelix, he's a member of her crew, and she is the Captain, without contact with her superiors, she is Judge, Jury and Executioner on her ship. Now, of course, if/when they make it back to Federation Space, she could be Court Martialed for any judgements/actions she took that Starfleet might disagree with, but, as long as she's top dog, it's her ship, and she can do as she pleases.
Now of course, this doesn't make immoral acts moral, it only states she is at this time, the ultimate authority on her ship.
However, I don't think her decision to save Neelix and Tuvok by sacrificing Tuvix was immoral.