Bringing Pets With You

We may possibly be moving to Port Moresby and I am wondering if anyone on the forum can give me advice on this topic.  I have a very tiny dog and I know I can arrange flights to Australia where I'll be able to keep her with me in the cabin. This is important because she has to have her anti-seizure meds every 12 hours plus she gets very afraid easily.  I don't think she'd do well at all on the flight over.  I'm wondering if anyone knows of an airline from either Australia or New Zealand that will let me carry her in the cabin with me to POM.  Another concern is that I've heard that to bring a pet into PNG, you have to go through a quarantine period.  I've heard that New Zealand has a much shorter one than Australia.  So any advice you have about that would be appreciated.  And finally, does anyone have experience with the veterinarians in Port Moresby?   Thank you so much.