I agree that, if this becomes a long-term thing, you may grow out of the DADT thing. You might want a bit more information and the security of knowing a bit more about what she's doing.
But for now, when you've just been on one date? This is casual! I'm not sure if it's important that you meet whole scores of other people when you're just getting to know her.
How many people want to meet the extended family of a first date?