In Shrodinger's cat, it seems our ignorance of the cat's state of existence places the cat in superposition of being in both states simultaneously. But since all of us exist in a state of not knowing when and how we are going to die, does that mean we also exist in superposition?
The Shrodinger's cat is a thought experiment. In QM there are several interpretentions and some of these does not require the "collapse of the wave function". So QM is an established theory of the quantum level but it is not a completed theory so the hypothesis that we may derive from each interpretention are nothing else than hypothesis without any real value. So yes according to an interpretantion of QM we exist in superposition but this is an ampty idea in essense.
Let's assume your interpretation of quantum mechanics for the sake of the argument.
The cat is in a superposition because we do not know if it is alive or dead. Now you don't know when and how your future self will die, so it's your future self, not you now, that could be in a superposition by this standard.
Also, note that not everything we don't know about is in a superposition, because someone else might know about it (again, following your interpretation of quantum mechanics). So if someone in the future knows how and when you die, then your future self is not even in a superposition.
You could reply that future observers don't exist yet, so that nobody actually knows when and how you will die. But if you follow this line, your future self doesn't exist either, so is not in a superposition.
So any way you think about it, the answer is: no, from the fact that you don't know when you will die does not follow that you're in a superposition.
I don't think this sort of attempted analogy between a physics thought exercise and philosophy works exactly, nevertheless it made you think about this question so it must have done some good. So to continue your analogy I would have to say that we have to make a good observation of our lives as we go along and in essence collapse our own wave function. In Sartre this would be through commitment to some purpose or interest (it can even be jazz music as in his novel Nausea, if memory serves), Heidegger would say perhaps our own way of being-towards-death. It seems to me you have noticed that human freedom offers so many at least theoretical opportunies that we could easily lose ourselves to ideterminancy unless we commit ourselves in some way. So you may be interested in the existentialist school. P.s. I can know with a high degree of precision when I will die if I take my own life, but I'm not willing to go that far for knowledge! There are just things we don't know about our future, we don't know but at least we know we don't know. I'm not sure we need the word superposition. I would not add extra words when we have enough words in philosophy as it is.
The mathematical concept of superposition is not the same as not knowing. Schrodinger's cat is a frustrating topic for a novice in QM to explore because the whole reason Schrodinger invented it was to poke at the uncomfortable claims that the Copenhagen Interpretation required. Its job is to cause difficult questions to come forth.
As for the cat, the Copenhagen Interpretation states that the cat is in a superposition of alive and dead until it is observed. Observation is a very nuanced concept in Copenhagen, which is not the same thing as us knowing or not knowing. It is closer to answering the question of whether or not the information exists to be known or not. Until the observation, that information does not exist. This is different from a simple "we don't know if we're alive or dead."
Other interpretations have different solutions to this puzzle. Multiple-Worlds Interpretation, for instance, states that we can't objectively talk about the state of the cat, but we can talk about the combined state of the observer and the subject: "the observer's observed state of the cat will be consistent with the actual state of the cat."
Pure quantum mechanics, without the aid of an interpretation to bring it into the more classical-framed ways of viewing the world, would argue that everything is part of a quantum mechanical "wave function." This function can be decomposed into superposed states, if desired, but that's about as far as it goes. To explore your question in this realm, we would have to dive deep into what does the "we" in "do we all exist" actually means. It turns out that it can be harder to pin down than you might like.
It is a fun thought process to work through, but it's not the same as uncertainty about one's own death.