My dogs have moved from Hawaii to Seattle to Japan to here in
So. Cal. Both are not the friendly kind of dogs, to my
disappointment. Anyway, I don't think they had any problems
adjusting. My older dog, suay suay, caught a virus leaving Japan,
and then caught two more on our drive here from Seattle. Cost us
$10K to nurse him back to health. (Very long story and no I'm not
rich. I'm beyond broke.) Other than that, they are fine.
Your cat will be fine. It's only the plane ride that may be the
hardest on her. Surprisingly, both my dogs didn't even let out a
whimper on the plane. Even the flight attendant said they were much
better than the young kids on the flight. 
Thanks jetta. Found out from AVA that my cat will not be
quarantined. I was worried about the quarantine part. As for the
climate change, guess have to put her in ac room for a while. Seems
that there is a heatwave in S'pore...