Phuket Air...Who are they?
 

Cheap flight sydney-london is currently being offered
Qantas to BKK then BKK london by Phuket

are they a charter outfit?

Phuket Air ( or Phuket Airlines, depending what day it is ) operated a couple of 737-200s on some domestic routes, then they bought a few months back some Namsc-YS11's ( aircraft buffs will be surprised no doubt to see these aircraft are still flying ) which they are stopping using.
They recently bought some ex KLM 747-300s and have just launched a Bangkok-Chittagong(Bangladesh)-Dubai Route and apparently are starting flights between Bangkok and Gatwick. That's about all I can tell you.

OK -- how does one pronounce "Phuket"?

Poo-KET of course.