I just came back from overseas trip with my family. My wife is an Australia PR and she doesn't want to get an Australian citizenship. She just get her new passport recently and have not link up her PR status into her new passport yet. Ooops....I am registered migration agent and didn't do this for my wife.....LOL. Guess that it would be just fine carrying both old & new passport when travel.
Aha... traveled out from Australia is OK. But once she wanted to checked in with Qantas on the way home. Qantas staff cannot issue her a boarding pass until her PR is linked up to the new passport which Qantas staff can get this done over the check-in counter easily. Just key in her detail electronically and send it to Canberra. Qantas staff advised us that, the waiting period is about 20-30 minutes which we didn't mind at all. We got plenty of time in our hand... :)
Surprisingly, Canberra get back to Qantas staff (either by fax or electronically I am not sure) within 5 minutes which was quite fast.
The moral of story is "Always" update your new passport detail with the Department of Immigration before you travel, so you won't be stopped at the check-in counter at the airport... :)