As tifters said, quite painless IF you have all the right paperwork -believe me they love paperwork here.
We used Jet Pets.
Don't know how they compare pricewise with others but they were excellent.
Picked the cat up at our apartment a few hours before our flight for final vet check, put her on the same flight as us. On arrival I went straight to opposite side of the airport (which is harder than it sounds here) and cleared her through AFCD. Home the same night. About AUD700 if I recall.