We live in Cardiff and my wife teaches in Caerphilly (she teaches primary). I'm the one who sometimes works in Swansea. My advice would be to go on the reccie and see what kind of feel you get for the place - where are you staying?
We spoke to some 'pom' teachers who have recently moved out there and they have had no problems finding supply (they call it relief teaching), but permanent jobs are pretty thin on the ground unless you want to live in a rural area. The rates of pay for relief teaching are really good though. From $285-$412 per day, here is the link: