Australia, New Zealand & the South Pacific - How does an ETA work?

Sorry for what is probably a stupid question but here goes.

When I show up for my flight from LAX-AKL (or AKL to SYD, not sure if they'll check for the former flight since I have about a week in NZ), how does Qantas know I have an ETA?

The reason for my question is this: I got an ETA before I booked tickets. I got the ETA through the official site for it. I then booked tickets (AA tickets, QF flights and flight numbers). I called AA today and they said there was no way for them to look up ETAs and I'd need to get a new one through them. Um...that doesn't make sense! :rolleyes:

The agent then told me to just go to the Qantas counter and show them my visa. :rolleyes: That doesn't make sense either since its electronic! All I have is a confirmation number.

So...I assume Qantas will be able to see I have an ETA so I can fly, or do I really have to get another ETA even though I have a valid one now?

Thanks!

Any airline can check through the CRS - they enter your full name, passport number and passport expiry date, and if it matches the details you provided when you applied for the ETA then the system will advise that there is a valid ETA.

Dave