My girlfriend is curious about how flexible the pen and paper RPG hobby that I love can be, so I asked her what scenario or theme that she would like to be/live in her dreams. She said something like, to live underwater like a fish, looking for food and a partner to have a family, and running from predators.
It's a really hard challenge: I'm trying to find an existing one but it seems there is none. So I'm creating one from scratch (when I have the time to do so). Are there any games like this, or alternative suggestions I should consider?
I have never used a game to do this particular kind of game, but there is a category of games that I know are designed specifically to do this kind of thing, and I know of game systems in the category that could easily handle it. There is a category of games that are specifically designed to handle "anything", and more-or-less manage to do it. These "generic" or "universal" game systems vary in how much detail they handle mechanically, from extremely detailed simulation-type systems to extremely loose narrative-type systems.
I can't recommend any that I know would work for this because I haven't done it (although I have my strong educated guesses about which would work) and the differences between them are a strong matter of individual taste—and I don't know you or your partner's tastes. However, I can link you to Wikipedia's article on generic role-playing game system, which lists several of the most well-known. Several have free "lite" or "quickstart" versions that you can download, or have editions that are entirely free.
I would advise doing some reading on a handful of those to find one that sounds like it could handle this. I find reviews of games to be the most informative for determining suitability for my game ideas. RPG.net has a searchable library of reviews that is both comprehensive and in-depth, covering more games than I sometimes can believe even exist in the first place.
Of course, you could still make your own RPG to directly implement a game like this. That's definitely one way to demonstrate that roleplaying games can be about anything! I've tried my hand at game design and it's not nearly as easy as it seems, so I would personally hesitate to design a game when winning my partner over to the RPG side is on the line; but if you have a knack for it, you may be able to create a better-tuned experience than a generic universal roleplaying system. I would personally go with the existing system, but only you can judge how you're best equipped to proceed, so don't let my judgement from a distance override your own good sense.