I think it was rather presumptuous of your friend to ask if you could take her TO the airport and then just make a statement that assumed you would pick her up again when she got back.
I don't think it's terrible to bow out. "Sorry, 6 AM is too early for me. I can take you there on X date but you'll have to make other arrangements for Y date." I bet nobody in her family or close circle of friends is willing to do this, which is why she pulled the, "Oh, by the way, you're picking me up at 6 on the return trip" routine. But you know what? I can't think of an airport anywhere that wouldn't have taxis, shuttles, and/or access to public transit. People can get themselves home from airports without inconveniencing friends.
Or, can you play dumb? "So, friend, I'm calling to confirm about your departure so I can plan the rest of my day. So I pick you up at X time on X date, right? Your flight's at noon? Great, that's what I thought. See you then. What arrangements did you make for pickup when you get back? What? Me? Oh, I'm sorry, I think there was a misunderstanding. You asked me to drive you TO the airport. I'm afraid it won't be possible for me to go pick you up when you get back. Probably best to get a cab, if you can't find a family member to pick you up."