I've had younger friends before, without even thinking of the potential public view. No issues, it was strictly platonic. In fact, the fact that it was completely friends is probably why it didn't even occur to me that someone could find it weird.
Having said that, I think that this could go very badly for you for several reasons. First of all, you wouldn't have asked if you didn't think there was some potential problems. The second issue is what others have mentioned, what if you turn her advances down? She might say it was all your idea, etc. Even if initially you meet her parents and everyone is cool, they might trust you enough that the two of you could hang out alone. In that case it opens the problem of accusations.
Finally, I would be most worried if I were you based on the fact that she didn't want to tell her parents. If she didn't want them to know, there might be a good reason for that. Either she wants there to be more than friendship or maybe her parents are the overprotective type who wioll kill you for accidental contact that they misinterpret.
I'm not saying don't do it, but I would difinitely say it has more bad potential than good. Be careful if you go through with it.