They don’t die that fast, but there’s two major things working for you here. First is that there are very few sperm in pre-cum to begin with. They may be present, and it’s technically possible to get pregnant from it, but it’s highly unlikely that there’s many viable sperm and they’re capable of getting where they need to go, especially just from hitching a ride on your fingers. Along these lines, while it may be true that sperm dies on contact with air (and, as a biochemist, I’m very skeptical of that claim), keep in mind that most sperm, even in pre-cum, is not exposed to air, they’re in the protective solution that is cum. But still, there’s not much there to begin with in pre-cum.
Secondly, the chances of getting pregnant when you’re trying are surprisingly low, something like 20% even if you know she’s ovulating. Sperm have literally a several-day journey to make after ejaculation, replete with choices to be made about direction of travel. Along these lines, cum has various properties that help sperm survive for the several day journey, as the vagina is a surprisingly inhospitable place for sperm. Pre-cum has far less of this, and thus you have far, far less sperm, in a worse environment, and already with a low chance of finding an egg, and even then, a small chance of implanting (iirc, it requires quite a few sperm to find the egg, as the first ones weaken the barriers to allow the later sperm to enter). So, yeah, I wouldn’t worry at all. And I’d actually say the chances of being struck by lightning tomorrow are a decent sight higher.
This is not to say never worry, and it’s very good you’re thinking about it and that you came to ask (and this is certainly not true for real sex, as 20%, while I consider surprisingly low, is way higher then any teen should want to gamble on). But I don’t think you have anything to be concerned about. I would say having condoms is never a bad idea (and hey, if you both decide to move forward, you’re prepared!), and you could bring up the idea of hormonal birth control with her (someday, we will have male chemical bc. Someday…). This depends a lot on your age and her parents, probably, but it’s usually not a bad idea, some have a number of side benefits like depo-provera and the pill, and most are even better than condoms in terms of pregnancy prevention (though, in general, I’d suggest both if you do actually go to sex).
Also, i highly suggest you check out Scarleteen in general, which is a fantastic site for sex ed.