random depression is random. not much you can do about it other than lessen your daily worries one by one, so that depression doesn't get too much to feed on. most of my random depressions disappeared when i got a good job, even more are disappearing as i adjust to my work situation and start feeling like i can handle it. there's still a lot left, but i haven't felt like ceasing to exist in several months now.
of course i still get down, but just knowing that it'll pass makes it easier to just let it happen, and continue my life while waiting for brighter days. those random depressions aren't always triggered by something easily identifiable, but just trying to find the cause might also help. right now we're a day or two after a full moon, and these days always make me anxious or depressed with no other reason than the moon starting to disappear again. the days just before new moon are worse still, but how bad seems to depend mostly on whether i have worries to feed depression and anxiety or not.
study your own depression cycles like many women study their monthly cycles. write down on your calendar when it starts and ends, and whether there was anything triggering it or not. finding a pattern can be interesting, but not finding one can be just as interesting. looking at my own random depression cycles/mood swings as some kind of interesting natural phenomenon to be studied made it a little more easy to bear, since i acknowledged that it isn't necessarily me there's something wrong with. my body/brain just reacts oddly to changes in my environment, and making the right precautions can help lessen depression when it hits.
and if that doesn't help, think of your poor cat. you can't cease to exist, since science can't do that quite yet. if you die, your existence will always be remembered by part of the world, and it would confuse or even devastate your cat. poor innocent little thing wouldn't understand suicide or other sudden death. and remember that death is a once in a lifetime experience, it should be enjoyed at the content and rather happy end of your life, rather than rushed.