Uhh, well firstly if you've been texting her for a month without asking her out, then you are very much invested, and you haven't had sex. So that's a recipe for problems. By all means go ahead and move forward with her, but do not be disappointed if it does not go the way you hope. In that case just ask another girl out without investing so much first. The problem with your current situation is you're thinking "I really like this girl and I don't want to mess it up" = "I've invested a lot in this girl and gotten nothing much yet, I want to get a return on my investment". This makes it very hard to play it cool, be a bit aloof and see where it goes and not worry too much either way -- what often happens is that we try too hard to engage her, qualify ourselves, we're nervous on the date, etc. As long as you watch out for these problems and correct accordingly, you'll be okay.
Anyway, you might be friendzoned or you might not. It really depends how much she liked you in the first place. If she wasn't too sold on you but decided to give you a chance, and has subsequently discovered you have a lot of friend value and not much lover value, you might be in trouble. If she really liked you from the first meeting, then you might have disqualified yourself as a lover but still qualify as a boyfriend. In that case, expect her to put up a lot of resistance to sex on the first date, and to make you work quite hard to bed her. As a novice that's not really a bad thing, it just means you have to take her on some more dates etc. But what would you be doing anyway... sitting at home? So no problem. I suggest you read
this article on date compression, and put it in your toolkit, just in case it turns out you need it.
The way you asked her out was perfect. Ultra casual, it's just a hangout... when you get to a more advanced level you'll be able to ask her out in this ultra casual way, and still have her understand that you're very sexually interested (through your body language), the risk you take at a more novice level is she might think it's just a friendly hangout. For example if something is a "study date" she might take it literally and then be upset and surprised when you go to kiss her. So as a novice it can be better to make your intentions more explicit, but I wouldn't sweat it. The best kind of dates are hangouts in which "sex just happens". In this case. from what you've said, I think she'd have to at least have the possibility in her mind that you might be planning to escalate, so you're in pretty good shape here. Just go on the date, build connection with her (by talking and expanding on the subjects you've already discussed, and having good body language and eye contact etc)... and try to get her alone.
It sounds like you'll already be alone, because you'll be backroading... so all that remains is to kiss her, if that's a problem she'll let you know, but otherwise
assume attraction. Go in confidently and you'll be golden

How you work it exactly, is something you should think about ahead of time, like maybe pack a picnic and pull over somewhere remote to eat, and kiss her then? I would probably try to do this in the first half-hour or so, if you wait too long she may go cold and put up lots of resistance.
Ray